Building designed for performances, or part of one (12)
I believe the answer is:
Here is my best explanation:
'building designed for performances or part of one' is the definition.
This is the entire clue.
(Other definitions for amphitheatre that I've seen before include "Roman tiered arena", "Arena; gallery tier", "Large oval stadium with tiers of seats", "Classical home for drama", "Theatre gallery seating area", "Open auditorium" and "Classical performance area".)