Regret being outside the church with a bit of lace (5)
I believe the answer is:
ruche
'a bit of lace' is the definition.
The definition suggests a singular noun which matches the answer.
'regret being outside the church' is the wordplay.
'regret' becomes 'rue' (to rue something is to regret it).
'being outside' means one lot of letters goes inside another.
'the church' becomes 'ch' (common abbreviation).
'rue' enclosing 'ch' is 'RUCHE'.
'with' is the link.
Can you help me to learn more?
(Other definitions for ruche that I've seen before include "Decorative frill" , "Pleated strip of material" , "strip of lawn?" , "Piece of lawn" , "Fabric frill or pleat" .)