. . . name provided on stage quicker (7)

I believe the answer is:

niftier

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'quicker' is the definition.
Both the answer and definition are comparative adjectives. Maybe they are linked in a way I don't understand?

'name provided on stage' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'provided' becomes 'if' (eg 'provided it's sunny' means 'if it's sunny').
'on' means one lot of letters go next to another.
'stage' becomes 'tier' (I've seen this in another clue).
'n'+'if'+'tier'='NIFTIER'

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I've seen this clue in The Guardian.

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