Hastily fasten bridle, etc (4)
I believe the answer is:
tack
I believe this is a double definition.
'hastily fasten' is the first definition.
(tack can mean to fasten quickly or temporarily)
'bridle etc' is the second definition.
(I know that bridle is a type of headgear)
(Other definitions for tack that I've seen before include "Staple - food" , "Nail; course of action" , "(Of a sailing ship) alter course through the wind" , "Stable gear" , "Nail - windward course - temporary stitch" .)