Encourage popular father to keep first of promises (7)
I believe the answer is:
inspire
'encourage' is the definition.
(I know that inspire is a type of encourage)
'popular father to keep first of promises' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'father' becomes 'sire' (synonyms).
'to keep' means one lot of letters goes inside another.
'first of promises' becomes 'p' (1st letter of 'promises').
'sire' going around 'p' is 'spire'.
'in'+'spire'='INSPIRE'
(Other definitions for inspire that I've seen before include "Encourage - animate - draw into the lungs" , "move!" , "Galvanize" , "Fill with confidence - be the origin of" , "take a breath" .)