Keen on headless horse (4)
I believe the answer is:
into
'keen on' is the definition.
(I've seen this before)
'headless horse' is the wordplay.
'headless' means to remove the first letter.
'horse' becomes 'pinto' (pinto is a kind of horse).
'pinto' with its initial letter taken off is 'INTO'.
(Other definitions for into that I've seen before include "Fascinated by" , "Two -- six is three" , "Teachers' trade union" , "Not I (anag.)" , "Curious about" .)