In favour of a short nudge (3)
I believe the answer is:
pro
'in favour of' is the definition.
(I've seen this before)
'a short nudge' is the wordplay.
'a short' means to remove the last letter.
'nudge' becomes 'prod' ('prod' can be a synonym of 'nudge').
'prod' with its final letter removed is 'PRO'.
(Other definitions for pro that I've seen before include "One doesn't play just for the love of it, in short" , "Favouring the professional" , "Golfer" , "Of argument, say, in favour of" , "Top player" .)