Material in provincial theatre restricted by Church (5)
I believe the answer is:
crepe
'material' is the definition.
(crepe is a kind of material)
'provincial theatre restricted by church' is the wordplay.
'provincial theatre' becomes 'rep' (a local repertory theatre).
'restricted by' means one lot of letters goes inside another (I've seen this in other clues).
'church' becomes 'CE' (abbreviation for Church of England).
'rep' going inside 'ce' is 'CREPE'.
'in' is the link.
(Other definitions for crepe that I've seen before include "Thin wrinkled fabric" , "Thin twenty four Ac" , "Crinkled paper or fabric" , "Flat French food" , "Crinkly material" .)