Encourage the family poet (7)
I believe the answer is:
pushkin
'poet' is the definition.
(I know that Pushkin is a poet)
'encourage the family' is the wordplay.
'encourage' becomes 'push' (I've seen this in another clue).
'the family' becomes 'kin' ('kin' can be a synonym of 'family').
'push'+'kin'='PUSHKIN'
(Other definitions for pushkin that I've seen before include "Boris Godunov poet" , "Russian poet, author and dramatist" , "As writer" .)