Juvenile horse last in race after support on course (7)
I believe the answer is:
teenage
'juvenile' is the definition.
(I've seen this before)
'horse last in race after support on course' is the wordplay.
'horse' becomes 'nag' (term for an old horse).
'last in' says to take the final letters.
'after' is a charade indicator (letters next to each other).
'support on course' becomes 'tee' (golf tee on a golf course).
The final letter of 'race' is 'e'.
'nag'+'e'='nage'
'nage' after 'tee' is 'TEENAGE'.
(Other definitions for teenage that I've seen before include "Like a category of youngsters" , "Youthful" , "Relatively young" , "Adolescent" , "Gee, neat (anag)" .)