Town square briefly quiet in the morning (7)
I believe the answer is:
evesham
'town' is the definition.
(I've seen this before)
'square briefly quiet in the morning' is the wordplay.
'square' becomes 'even' (both mean 'owing nothing' as in 'we're all square').
'briefly' means to remove the last letter.
'quiet' becomes 'sh' (both can be said to tell someone to be quiet).
'in the morning' becomes 'am' (AM on a clock).
'even' with its final letter taken away is 'eve'.
'eve'+'sh'+'am'='EVESHAM'
(Other definitions for evesham that I've seen before include "River Avon town" , "Town near Worcester" , "place" , "mediaeval battle" , "market town" .)