Have parent stay silent (4,3)
I believe the answer is:
keep mum
'stay silent' is the definition.
(I've seen this before)
'have parent' is the wordplay.
'have' becomes 'keep' (keeping is a kind of having).
'parent' becomes 'mum' (mum is a kind of parent).
'keep'+'mum'='KEEP MUM'
(Other definitions for keep mum that I've seen before include "Don't tell a soul" , "Remain silent" , "(don't mention it)" , "Stay silent" .)