First cake Alice baked for gluten-intolerant chap (6)

I believe the answer is:

celiac

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

'gluten-intolerant chap' is the definition.
I can't judge whether this defines the answer.

'first cake alice baked' is the wordplay.
'first cake' becomes 'c' (1st letter of 'cake').
'baked' indicates an anagram.
'alice' is an anagram of 'eliac'.
'c'+'eliac'='CELIAC'

'for' is the link.

Can you help me to learn more?

(Other definitions for celiac that I've seen before include "about tummy" , "about US corporation" .)

I've seen this clue in The Hindu.

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