Checks on the horses (5)
I believe the answer is:
reins
'checks' is the definition.
(reining is a kind of checking)
'on the horses' is the wordplay.
'on' becomes 're' ('on' can be mean 'with reference to').
'the horses' becomes 'ins' (I can't explain this - if you can you should believe this answer much more).
're'+'ins'='REINS'
Can you help me to learn more?
(Other definitions for reins that I've seen before include "Straps to control" , "Means of control for a horse" , "Harnesses" , "Power to direct and control" , "They're used to control" .)