Strap attached to a bridle (4)

I believe the answer is:
rein
'strap attached to a bridle' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for rein that I've seen before include "Harness item" , "Long strap to restrain" , "Leather used for control in horse-riding" , "Part of tack" , "Director's power" .)