A function originally held in church eating-place (4)
I believe the answer is:
cafe
'eating-place' is the definition.
(type of eatery)
'a function originally held in church' is the wordplay.
'originally' indicates taking the first letters.
'held in' indicates putting letters inside.
'church' becomes 'CE' (abbreviation for Church of England).
The first letter of 'function' is 'f'.
'a'+'f'='af'
'af' going within 'ce' is 'CAFE'.
(Other definitions for cafe that I've seen before include "Inexpensive restaurant serving light refreshment" , "in which one had a meal?" , "It's an eating house - face up to it" , "Place to eat" , "Small tea shop or restaurant" .)