A small horse and that's a drawback (4)
I believe the answer is:
snag
'a drawback' is the definition.
(I've seen this in another clue)
'a small horse' is the wordplay.
'a small' becomes 's' (abbreviation - e.g. clothes size).
'horse' becomes 'nag' (term for an old horse).
's'+'nag'='SNAG'
'and that's' acts as a link.
(Other definitions for snag that I've seen before include "ladder" , "Complication, drawback" , "Rip or tear" , "Minor hitch" , "Hitch, unexpected problem" .)