In Israel in as shul that has two shacharis minyanim one after the other, a kohen comes in for the second minyan just as the first minyan is coming to the priestly blessing. Should this kohen perform the priestly blessing for the first minyan?
It's strongly implied (S"A O"C 128:2) that if a Kohen is in the room when the Chazzan calls "Kohanim" (or some other form of the Kohen being called up to give the blessing), he has an obligation to say the blessing and violates a Mitzvah if he does not.
The Chayei Adam writes (32:28) that a Kohen who hasn't prayed yet and is by a Minyan that is up to Birkas Kohanim should do the blessing then and pray afterwards. While it doesn't explicitly describe what the law would be if the Kohen plans on being at a later Minyan, taking these two sources together, I would suggest that if a Kohen is at an earlier Minyan and is in a scenario where he gets 'called up' to do Birkas Kohanim, he would have an obligation to do so.
There is also a Beiur Halacha on S"A O"C 128:4 that implies that one should not put himself in a scenario where he is exempting himself from doing the Mitzvah of Birkas Kohanim, although admittedly that might not apply in this scenario where the Kohen is intending to do the Mitzvah later.
It would seem based on this that the ideal situation would be for a Kohen to not put himself in a situation where he gets an obligation to say Birkas Kohanim. There are a handful of scenarios that obligates a Kohen to do Birkas Kohanim, recounted at the end of O"C 128:4. Therefore it would seem that perhaps waiting outside the sanctuary or in a side room until after Chazaras Hashatz would be preferred.
Note that the other way around (where the Kohen has already done Birkas Kohanim and happens to be in another Minyan later), the Kohen does not have to do Birkas Kohanim again (S"A O"C 128:3).