Private Victor, heading off (5)
I believe the answer is:
inner
'private' is the definition.
(as in one's private or inner thoughts)
'victor heading off' is the wordplay.
'victor' becomes 'winner' (synonyms).
'heading off' means to remove the first letter.
'winner' with its initial letter removed is 'INNER'.
(Other definitions for inner that I've seen before include "closer than magpie" , "More secret, private" , "Annulus nearest bull" , "pretty good shot" , "Esoteric" .)