A short time in that place's playhouse (7)
I believe the answer is:
theatre
'playhouse' is the definition.
(thesaurus)
'a short time in that place's' is the wordplay.
'short time' becomes 't' (abbreviation for time).
'in' means one lot of letters goes inside another.
'that place' becomes 'there' (I've seen this before**).
'a'+'t'='at'
'at' inserted into 'there' is 'THEATRE'.
(Other definitions for theatre that I've seen before include "Space for 11 across art" , "Drama in general" , "Show" , "A tether (anag.)" , "Where you might find ham" .)