Cheers enveloping Irish after clinching a triple crown (5)
I believe the answer is:
tiara
'triple crown' is the definition.
(thesaurus)
'cheers enveloping irish after clinching a' is the wordplay.
'cheers' becomes 'ta' (I've seen this in other clues**).
'enveloping' indicates putting letters inside.
'irish' becomes 'ir' (abbreviation).
'after clinching' is an insertion indicator.
'ir' going around 'a' is 'iar'.
'ta' placed around 'iar' is 'TIARA'.
(Other definitions for tiara that I've seen before include "Item of jewellery" , "Woman's crescent-shaped ornamental headdress" , "Half a crown!" , "Pope's triple-tiered crown" , "It might go to one's head" .)