Victor loses his head nearer the centre (5)
I believe the answer is:
inner
'nearer the centre' is the definition.
(I've seen this before)
'victor loses his head' is the wordplay.
'victor' becomes 'winner' (synonyms).
'loses his head' means to remove the first letter.
'winner' with its initial letter taken off is 'INNER'.
(Other definitions for inner that I've seen before include "Ring next to the bullseye" , "closer than magpie" , "Interior" , "More secret, private" , "Situated inside" .)