Artificial fibre seen in a church gallery (7)
I believe the answer is:
acetate
'artificial fibre' is the definition.
(acetate is a synthetic material)
'a church gallery' is the wordplay.
'church' becomes 'CE' (abbreviation for Church of England).
'gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'a'+'ce'+'tate'='ACETATE'
'seen in' acts as a link.
(Other definitions for acetate that I've seen before include "Transparent film" , "It once covered records" , "(Chemical used in production of) clear film" , "Textile fibre, plastic" , "Transparency used with an overhead projector" .)