Popular father retaining power to encourage (7)
I believe the answer is:
inspire
'encourage' is the definition.
(inspiring is a kind of encouraging)
'popular father retaining power' is the wordplay.
'popular' becomes 'in'.
'father' becomes 'sire' ('sire' can be a synonym of 'father').
'retaining' means one lot of letters goes inside another.
'power' becomes 'p'.
'sire' going around 'p' is 'spire'.
'in'+'spire'='INSPIRE'
'to' is the link.
(Other definitions for inspire that I've seen before include "Breathe - fire" , "Excite" , "Animate (with feeling)" , "Motivate" , "Give (feeling of) creativity to" .)