Claim sty had become spiritual (8)

I believe the answer is:

mystical

I'm a little stuck... Click here to teach me more about this clue!

'spiritual' is the definition.
(thesaurus)

'claim sty had' is the wordplay.
'claim sty' anagrams to 'MYSTICAL'.
However, I'm unsure how this is indicated.

'become' acts as a link.

Can you help me to learn more?

(Other definitions for mystical that I've seen before include "Having a spiritual significance" , "Occult, spiritual" , "Sacredly obscure" , "of occult rites" , "wonderful" .)

I've seen this clue in The Daily Express.

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