Say Iranian forces manage to overrun Iraq by 1983 and establish a puppet Islamic republic.
What would be the geopolitical impact of this.
Enormous; Iran would become the Big Dog of the Moslem Middle East.
Kuwait would be terrified; also Saudi Arabia. They would have to make formal defense arrangements with a real military power, probably the US. If the US balks, then maybe Pakistan, with the Arabs paying all the bills and then some - basically a mercenary army deal.
A big question is when Iran wins. The war started in September 1980, during the US/Iran hostage crisis. At that time, Iran's armed forces were seriously disrupted by the Khomeinist revolution and subsequent purge of Pahlevi loyalists. I don't see Iran counterattacking successfully until mid-1981 at the very earliest.
So it would be the Reagan administration making any deals, and IMO Reagan would go for it. This in turn could have knock-ons with the development of militant jihadism in the Kingdom, as the presence of "infidel" Americans would begin several years sooner. OTOH the much greater threat, from Shi'a Iran, might make the American presence acceptable to even hard-line Wahhabis.
Would it be likely to see Iranian troops move into Syria.
OTL there is now a large Iranian presence in Syria, fighting the on-going rebellion. Strongman Bashar Assad accepted this out of necessity. I don't think Hafez Assad (Bashar's father and predecessor) would do so. At that time Syria coped with Islamist insurrection on its own (the Hama massacre) and there was no significant non-Islamist opposition.
However, with a land connection from Iran to Syria and maybe Lebanon, Iran might deploy troops to the Israeli border. As the Big Dog, Iran would be tempted to act on its proclaimed hatred for Israel, and Syria would welcome assistance on that front.
Things could get hot.
Another nut in the kernel is Kurdistan. AFAIK, there is no great conflict between the ayatollahs and Iranian Kurds. I could see Iran cutting a deal with the Kurds of Iraq, where they get a parastate in the north, provided they follow Iran's lead. However, this Kurdish parastate could easily become a base area for PKK operations in Turkey. That could bring Iraq and Iran into open conflict with Turkey and NATO.
If at the same time, Iran is inciting disorder in Kuwait, Saudi Arabia, and other Gulf states,
and threatening Israel - maybe there is an alt-Gulf War, with a US-led coalition of Arabs and NATO forces (and maybe Pakistan) moving to remove the Iranian theocracy and its satellite regimes. About this time the USSR would be falling apart, and make no trouble.