Alice pops out of the church (9)
I believe the answer is:
episcopal
'church' is the definition.
(I have seen 'Scottish Church' mean 'episcopal' so perhaps 'church' could also mean 'episcopal')
'alice pops out of' is the wordplay.
'out of' is an anagram indicator.
'alice'+'pops'='alicepops'
'alicepops' anagrammed gives 'EPISCOPAL'.
'the' is the link.
(Other definitions for episcopal that I've seen before include "sees can be described thus" , "Alice's pop? (anag)" , "run by bishops" , "controlled by bishop" , "Pepsi-Cola for bishops' kind of business" .)