I actually thought of this a while back. Here was my idea...
Season 1:
-The Enterprise-D is a new vessel in the year 2364, picking up his new officers at Farpoint Station. Things go as it did in the show, but Q gives a warning to Picard, "Live as you know it will change. A dark storm is coming to the Quadrant."
-The season goes as it went in our TL, a little cheesy, optimistic, showing that Starfleet has gone soft since the years of Kirk. It is a nearly imperfect world, with everything going well.
-Around three quarters into the season, tensions for the first time in decades flares up on the Romulan Neutral Zone. Tasha Yar and many members of the crew are killed during a Romulan attack, and four other Federation starships are destroyed. At the end of the season, it is revealed a nationalist coup occured on Romulus, prompting the incursion into Federation space.
Season 2:
-The season begins with the Romulan Cold War in full swing. Conflict is splitting apart the Federation and the crew of the Enterprise. The "Traditionalists", led by several elements of Starfleet Command who believe in the traditions of exploration and peace, fight against the "Modernists", who believe the Federation should militarize. In the Enterprise, the split is obvious, with Captain Picard and Data leading the Traditionalists, and Riker and Worf leading the Modernists. While not violent, it causes occasional strife in the crew when it comes to Romulans.
-Halfway through the season, Q sends the Enterprise thousands of lightyears from the Federation, where they make contact with the Borg. Due to the lack of preparedness, the ship is heavily damaged by the Borg, losing 150 officers in the process. Q returns the Enterprise to Federation space.
-The events of the Borg Encounter change Picard's view on the Federation. He soon becomes a modernist, believing that the Federation needs to defend itself. While the Borg Encounter had unified the Enterprise crew and most of the general population of Starfleet, the political sphere of the Federation is still split, and the risk of a Civil War within the Federation grows.
-In the season finale, the Federation President is assassinated by a traditionalist, sparking the Federation Civil War.
Season 3:
-After a month into the Federation Civil War, Admiral Hanson, with support from the Enterprise, take over Earth from the hands of the Traditionalists. After several battles early in the season, a truce is made after Romulan activity on the neutral zone increases.
-The Romulans sign a secret agreement with the Cardassians. The Federation at the same time organized an alliance with the Klingons. On Earth at the same time, Admiral Hanson is made President of the Federation.
-Riker and Troi get married during this season.
-After a devastating Romulan attack on Klingon colonies along the Neutral Zone, Worf returns to the Empire to assist in organizing a possible defense against the Romulans should a war break out.
-At the end of the season, the Borg attempt to attack Earth with a fleet of Borg cubes (3 cubes). Captain Picard is assimilated by the Borg, and becomes Locutus. This episode introuces Lt. Commander Shelby.
Season 4:
-The Battle of Wolf 359 takes place. Over 112 Federation ships are destroyed, and 25 Klingon vessels. The Borg are eventually taken out, but Picard is wounded. Picard is freed from the collective, but cannot command the Enterprise anymore. He is promoted to an Admiral by President Hansen (Which is met by much opposition by Starfleet officers, who still view Picard as Locutus).
-The Federation, following a major border incident with the Romulans, tear apart all previous agreements with the Romulans. Almost immediately, the Enterprise is armed with a cloaking device, and is ordered to go on a covert mission into Romulan space.
-The Enterprise under Riker's and Shelby's command moves into Romulan territory, where they find missing Ambassador Spock, who has helped organized a guerrilla movement on Romulus against the Romulan Empire. The Enterprise is discovered, and is forced to flee, but most of the guerrilla movement is wiped out.
-In the season finale, the Romulans have invaded the Klingon Empire and the Federation. The Romulan War has begun.
Season 5:
-A month into the war, Kronos falls to Romulan forces. The Chancellor is killed, leaving Worf one of the highest ranking officials in the Klingon Empire. Worf is made the Chancellor in an emergency meeting at Rura Penthe, the last stronghold of the Klingon Empire near Kronos.
-Alexander Rozhenko, Worf's son, is introduced into the series (For the sake of this series, he is in his early twenties in Season 5). He becomes the Tactical Officer in the Enterprise.
-The Enterprise faces defeat after defeat, and at the Battle of Vulcan, is forced to prepare for the defense of Earth. Deanna Troi, Riker's wife, is revealed to be pregnant. She returns to Betazed for safety during the war.
-During the season finale, the war comes to Earth. The Romulans enter the Solar System and take over several planets, before striking Earth. At the same time, the Cardassians invade the Federation, and take over Betazed.
Season 6:
-The Battle of Sol continues, with the Federation thanks to Klingon and Andorian reinforcements succeeding in repeling the Romulans. Much of Earth was damaged, and President Hansen was killed during a Romulan attack on Paris. Admiral Picard is made the President of the Federation, and promotes Riker to Admiral, making the Enterprise his flagship for the new 1st Fleet to deploy to the Cardassian Front. Lt. Commander Shelby is promoted to Captain as well.
-Riker is informed that Deanna Troi, her mother, and their 1 week old baby was killed during the Cardassian attack on Betazed. Riker goes into a rage, and orders a suicidal attack for his fleet into Cardassian territory, losing over a dozen ships under his command.
-Riker organizes after his failed attack a new offensive to capture Bajor, then move on into Cardassia. The attack on Bajor succeeds, and to make things better, the Breen attack the Cardassian Union, hoping to grab Cardassian territory in their weakened state.
-At the end of the season, Worf and Riker lead an attack to liberate Kronos. The battle is successful, but they find out that the population of many Klingon worlds were "Liquidated" by the Tal Shiar.
Season 7:
-Federation and Klingon forces move into Cardassian territory, capturing many border systems. After a month of heavy fighting, Cardassia is captured, forcing the Cardassians to the peace table.
-Data is captured during a Romulan attack into Federation space. They use his information stored in his brain to launch surprise attacks on Federation systems.
-In the middle of the season, the Romulan Empire falls into chaos as the Klingons under General Martok and Chancellor Worf move into Romulan space. The Romulan Civil War begins as well with the assassination of the main leadership.
-Borg attacks begin on Federation, Romulan, and Klingon space. Fearing the risk of invasion of the Alpha Quadrant, the Romulan War ends with an uneasy peace.
Season 8:
-Preparations are being made for the final showdown between the Alpha Quadrant and the Borg.
-The Borg invade Federation and Romulan space, starting the Borg War. Borg forces take over most Romulan territory, Borgifying Romulus.
-The Federation is once again beat back to Earth, but thanks to brilliant strategies from Captain Sisko, the Borg are beat back near the Moon. President Picard announces he will retire at the conclusion of the Borg War.
-The Borg War continues as Admiral Riker organizes a massive counter-offensive in the largest force ever amassed by the Federation. The Borg are beat back after heavy losses on both sides. At the end of the season, Romulus is liberated by Chancellor Worf, who announces the Klingons will annex over half of Romulan territory.
-The Borg during the season finale are beat back from Federation space. The war is considered generally over, but the Borg are still a lingering threat.
Season 9:
-President Picard retires, and is succeeded by President Paris, a former Starfleet Admiral. Admiral Riker feels that President Paris will not allow Riker to continue the attack into Borg space with the capture of a transwarp conduit into Borg space in the Delta Quadrant.
-Picard returns to the Enterprise at the request of Admiral Riker and Captain Shelby, and serves as an advisor for the two during the tumultuous times.
-Starfleet, or parts of it at least, start to continue exploration, including the Enterprise to an extent. Alexander Rozhenko is promoted to Commander, and becomes the First Officer on the Enterprise behind Admiral Riker and Captain Shelby.
-A new threat emerges from the Gamma Quadrant, the Dominion. While nothing comes of it yet, the next Star Trek series Deep Space 9 from the point of view of Commander Sisko will deal with them and the Dominion War.
-At the end of the season, Chancellor Worf retires, and is considered one of the greatest Klingon leaders since Kahless. The Klingon Civil War begins over succession as Worf returns to aid Riker in his plans.
Season 10:
-The entire original Enterprise crew is united once more. There, along with many Admirals and Starfleet officers, as well as Romulan, Klingon, Cardassian, and Breen leaders, the militaries plan a surprise attack through the Transwarp hub to wipe out the Borg homeworld.
-Preparations are being made for the offensive behind the back of President Paris. The Klingon government is too concerned with Civil War to go against Worf in his support of Riker, and the Romulans believe that the Borg are the ultimate threat. During this season, Q once again visits Picard.
-At the end of the season, the Battle of the Collective is launched. The largest fleet in Alpha Quadrant history is built from Federation, Klingon, Romulan, Cardassian, and several Breen ships, who cross into the Borg Transwarp Hub against the orders of President Paris. The final battle in the series starts, seeing the destruction of the Borg homeworld, and most of the collective. The Enterprise is heavily damaged during the battle.
-Riker and his fleet return to the Alpha Quadrant, victorious. Riker launches a coup against President Paris, and appoints a new Starfleet run government under Admiral Ross' command. Riker resigns from Starfleet, having nothing left to do. His wife has been dead for 5 years, as is his only son who lived a week. Shelby is promoted to Admiral, and Alexander Rozhenko becomes the Captain of the Enterprise, with Geordi LaForge as his First Officer.
-The series ends with the main cast on the Enterprise during a one-year reunion of the end of the Borg War. They play Poker, ending the 10 year series. The Enterprise, now repaired, prepares for new journeys under its new Captain and crew.