Look after relative and stay silent (4,3)
I believe the answer is:
keep mum
'stay silent' is the definition.
(I've seen this before)
'look after relative' is the wordplay.
'look after' becomes 'keep' (synonyms).
'relative' becomes 'mum' (mum is a kind of relative).
'keep'+'mum'='KEEP MUM'
'and' acts as a link.
(Other definitions for keep mum that I've seen before include "(don't mention it)" , "Stay silent" , "Remain silent" , "Don't tell a soul" .)