In some clubs it's an admission of formality (10)
I believe the answer is:
initiation
'formality' is the definition.
(thesaurus)
'in some clubs it's an admission of' is the wordplay.
I cannot really understand how this works, but
'in' is found in the answer.
'some' could be 'a' and 'a' is found within the answer.
'an' could be 'i' (Roman numeral for one) and 'i' is found within the answer.
'of' could be 'o' and 'o' is located in the answer.
'it' could be 't' (abbreviation. e.g. in 'tis) and 't' is found within the answer.
The remaining letters 'itin' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Another definition for initiation that I've seen is " Joining ritual; beginning".)