Nick’s not connected to church (5)
I believe the answer is:
notch
'nick's' is the definition.
(both can mean a small cut or impression)
'not connected to church' is the wordplay.
'connected to' means one lot of letters go next to another.
'church' becomes 'ch' (common abbreviation).
'not'+'ch'='NOTCH'
(Other definitions for notch that I've seen before include "Tallying incision" , "Snick" , "Make the cut" , "Secure" , "Mark indented in wood etc" .)