Sprint after European doctor for hug (7)
I believe the answer is:
embrace
'for hug' is the definition.
(to embrace someone is to hug them)
'sprint after european doctor' is the wordplay.
'sprint' becomes 'race' (I've seen this in another clue).
'after' means one lot of letters go next to another.
'european' becomes 'e' (abbreviation e.g. EU).
'doctor' becomes 'MB' (Bachelor of Medicine, Medicinae Baccalaureus).
'e'+'mb'='emb'
'race' after 'emb' is 'EMBRACE'.
(Other definitions for embrace that I've seen before include "Hold in one's arms" , "Take in arms" , "bear-hug?" , "Warmly welcome" , "Include - hug" .)