Crossword Genius

Sign me up to gain access to beauty contract (8)

Ross

I believe the answer is:

diminish

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

'contract' is the definition.
(I've seen this before)

'sign me up to gain access to beauty' is the wordplay.
I cannot really understand how this works, but
'me' could be 'mi' (both are spellings of the musical note) and 'mi' is located in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for diminish that I've seen before include "Make smaller or less" , "sink" , "cut down" , "get shorter" , "Diet" .)

I've seen this clue in The Times.
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