Time pressure on in playhouse (7)
I believe the answer is:
theatre
'playhouse' is the definition.
(I know that playhouse can be written as theatre)
'time pressure on' is the wordplay.
'time' becomes 't' (abbreviation).
'pressure' becomes 'heat' (I've seen this before).
'on' becomes 're' ('on' can be mean 'with reference to').
't'+'heat'+'re'='THEATRE'
'in' is the link.
(Other definitions for theatre that I've seen before include "where Finney played" , "Scene of plays" , "House" , "Globe, say" , "Place for operation or play" .)