Go on about quiet mum's cover-up (7)
I believe the answer is:
yashmak
'cover-up' is the definition.
(veil worn by some Muslim women)
'go on about quiet mum's' is the wordplay.
'go on' becomes 'yak' (both can mean to talk at length).
'about' means one lot of letters goes inside another.
'quiet' becomes 'sh'.
'mum' becomes 'ma' (synonyms).
'sh'+'ma'='shma'
'yak' placed around 'shma' is 'YASHMAK'.
(Other definitions for yashmak that I've seen before include "Face-veil for Muslim women like shaky ma" , "Am shaky about face-veil for Muslim woman" , "modest assumption" , "Veil concealing face worn by Muslim women" , "Facial veil" .)