Admit cutting last sound off (5)
I believe the answer is:
grant
'admit' is the definition.
(thesaurus)
'cutting last sound off' is the wordplay.
'last' indicates one should take the final letters.
'sound off' becomes 'rant' (to sound off is to rant or complain).
The final letter of 'cutting' is 'g'.
'g'+'rant'='GRANT'
(Other definitions for grant that I've seen before include "Bestow - Ulysses S. - Cary" , "Bestow; bursary" , "Give (a right, property, etc)" , "Permit" , "Concede, like an American general" .)