Character has ring that’s enormous (5)
I believe the answer is:
omega
'character' is the definition.
(letter of the Greek alphabet)
'ring that's enormous' is the wordplay.
'ring' becomes 'O' (letter resembling a ring).
'that's enormous' becomes 'mega' (I've seen this before).
'o'+'mega'='OMEGA'
'has' is the link.
(Other definitions for omega that I've seen before include "long letter" , "Athenian character" , "Greek long 'o'" , "symbol of resistance?" , "letter from abroad" .)