Not keen on horse trained overseas (8)
I believe the answer is:
offshore
'overseas' is the definition.
(both can mean in another country)
'not keen on horse trained' is the wordplay.
'not keen on' becomes 'off' (as in going off a particular food).
'trained' indicates anagramming the letters (to train can mean to grow something into a shape).
'horse' is an anagram of 'shore'.
'off'+'shore'='OFFSHORE'
(Other definitions for offshore that I've seen before include "No longer moored" , "Out of tax jurisdiction" , "Out to sea, away from land" , "abroad" , "In the main" .)