Claim sty had become awe-inspiring (8)
I believe the answer is:
mystical
'awe-inspiring' is the definition.
Both the definition and answer are adjectives. Perhaps you can see an association between them that I don't see?
'claim sty had' is the wordplay.
'claim sty' can be anagrammed to 'MYSTICAL'.
Though, I am unsure how this is indicated.
'become' is the link.
Can you help me to learn more?
(Other definitions for mystical that I've seen before include "Sacredly obscure" , "Inspiring spiritual awe" , "Inexplicable" , "Occult, spiritual" , "'Esoteric, spiritual (8)'" .)