Stay with mother and be quiet (4,3)
I believe the answer is:
keep mum
'be quiet' is the definition.
(synonyms)
'stay with mother' is the wordplay.
'stay' becomes 'keep' (keeping is a kind of staying).
'with' is a charade indicator (letters next to each other).
'mother' becomes 'mum' (mum is a kind of mother).
'keep'+'mum'='KEEP MUM'
'and' acts as a link.
(Other definitions for keep mum that I've seen before include "Don't tell a soul" , "Remain silent" , "Stay silent" , "(don't mention it)" .)