Hermit with strange cat is hanging around church (7)
I believe the answer is:
ascetic
'hermit' is the definition.
(I've seen this before)
'strange cat is hanging around church' is the wordplay.
'strange' indicates anagramming the letters.
'hanging around' is an insertion indicator.
'church' becomes 'ce' (abbreviation for Church of England).
'cat'+'is'='catis'
'catis' anagrammed gives 'astic'.
'astic' placed around 'ce' is 'ASCETIC'.
'with' is the link.
(Other definitions for ascetic that I've seen before include "Austere, Spartan" , "Mortifying the flesh" , "Abstemious, self-denying" , "Self-disciplined person" , "Self-denying, Spartan" .)