Volunteers to go back inside that place, a playhouse (7)
I believe the answer is:
theatre
'a playhouse' is the definition.
(thesaurus)
'volunteers to go back inside that place' is the wordplay.
'volunteers' becomes 'ta' (abbreviation for Territorial Army).
'to go back' says the letters should be written in reverse.
'inside' means one lot of letters goes inside another.
'that place' becomes 'there' (I've seen this before**).
'ta' written backwards gives 'at'.
'at' inserted inside 'there' is 'THEATRE'.
(Other definitions for theatre that I've seen before include "natural land formation?" , "US cinema" , "The rate (anag.)" , "(Military) field of action" , "A tether (anag.)" .)