Strap attached to a bridle (4)
I believe the answer is:
rein
<span class="explanation-format__ClueExplanation">'<span class="explanation-format__original">strap attached to a bridle</span>' is the definition.<br/ ><span class="explanation-format__explanation">(I've seen this in another clue)</span><br/ ><br/ >This is all the clue.<br/ ></span>
(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" .)