Does one stop in the middle of his silent shemoneh esrei when he hears birkas kohanim?
Please see our article here that dwells on this subject.
Modern-day authorities discuss the case of someone who is still davening the Amidah prayer when the Kohanim begin their blessing.
The Iggros Moshe writes that he should stop his prayer and focus on the blessing, a ruling seconded by the Shevet Ha-Levi. It is also quoted of the Chazon Ish that this is the right way to act.
Although Harav Elyashiv shlita, however, is quoted as opining that one should carry on one’s prayer uninterrupted. However, there are a number of possible proofs to Rav Moshe’s position, and as noted many side with his opinion.