Keep mum at home? Isn't to be kept in (8)
I believe the answer is:
maintain
'keep' is the definition.
(maintaining is a kind of keeping)
'mum at home? isn't to be kept in' is the wordplay.
'mum' becomes 'ma' ('ma' can be a synonym of 'mum').
'at home?' becomes 'in' ('in' can be similar in meaning to 'at home').
'isn't' becomes 'aint' (I've seen this before).
'to be kept in' is an insertion indicator.
'ma'+'in'='main'
'main' enclosing 'aint' is 'MAINTAIN'.
(Other definitions for maintain that I've seen before include "Assert" , "Keep going" , "Look after the upkeep" , "Keep (a building) in good condition" , "Conserve" .)