The opposite case, Elizabeth living till 1763 and continuing the fight against the haggard Prussians has been done several times, but I do not think the opposite case has been proposed. She was in periodic ill health throughout the 7 Years War.
So - first-level analysis - Peter takes the throne and pulls Russia out of the war with Prussia sooner.
How does Prussia react to a much earlier reduction in enemy pressure. Does it seek to get out of the war with a status quo antebellum peace ASAP? Or does Frederick have territorial ambitions, which may well succeed to Habsburg or Saxon territories (Saxony, Bohemia)?
I could see Fred being attracted to seizing both some of the Polish lands (West Prussia-Gdansk) and Saxon lands of the Wettin monarchs (maybe a decent fraction of Saxony.
How does this impact the rest of the 7 Years War in Europe and overseas.
Second-level analysis - how long does pro-Prussian Peter keep the throne? He was disliked by many, but perhaps with fewer Russian gains/victories his pro-Prussianism would be less resented? Did Catherine have the connections to succeed in a coup against her husband in the 1750s? What if she did?