What may be played in church or a pigpen, possibly? (4,5)
I believe the answer is:
pipe organ
'what may be played in church' is the definition.
(church organ)
'or a pigpen possibly?' is the wordplay.
'possibly?' indicates an anagram (I've seen 'possibly' mean this).
'or'+'a'+'pigpen'='orapigpen'
'orapigpen' is an anagram of 'PIPE-ORGAN'.
(Other definitions for pipe organ that I've seen before include "Musical instrument" , "Traditional church instrument" .)