Prove a sun exploded like this (9)
I believe the answer is:
supernova
'this' is the definition.
The definition suggests a singular noun which matches the answer.
'prove a sun exploded' is the wordplay.
'exploded' is an anagram indicator.
'prove'+'a'+'sun'='proveasun'
'proveasun' with letters rearranged gives 'SUPERNOVA'.
'like' is the link.
(Other definitions for supernova that I've seen before include "it puts an end to a starry career" , "Star made brilliant by stellar explosion" , "Exploding star that becomes extremely luminous" , "Star that explodes and becomes extremely luminous" , "cosmic explosion" .)