Start of theatre in the round; a building (7)
I believe the answer is:
rotunda
'building' is the definition.
(rotunda is a kind of building)
'start of theatre in the round a' is the wordplay.
'start of' suggests taking the first letters.
'in' indicates putting letters inside.
The initial letter of 'theatre' is 't'.
't' placed into 'round' is 'rotund'.
'rotund'+'a'='ROTUNDA'
(Other definitions for rotunda that I've seen before include "Do a turn (anag) -- circular domed building" , "Italian Pantheon, for instance" , "Round domed building" , "circular construction" , "Circular building with a dome" .)