Rider's requirement of rules for audition (5)
I believe the answer is:
reins
'rider's requirement' is the definition.
(something a horse rider needs)
'rules for audition' is the wordplay.
'rules' becomes 'reigns' (reigning is a kind of ruling).
'for audition' indicates a 'sounds like' (homophone) clue (audition can mean hearing).
'reigns' sounds like 'REINS'.
'of' is the link.
(Other definitions for reins that I've seen before include "water regulators?" , "Means of checking" , "Means of controlling a horse" , "They're used to control" , "Means of control for a horse" .)