If you want a trophy, start climbing higher (3)

I believe the answer is:

cup

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

'if you want a trophy' is the definition.
I can't judge whether this definition defines the answer.

'start climbing higher' is the wordplay.
'start' says to take the initial letters.
'higher' becomes 'up'.
The first letter of 'climbing' is 'c'.
'c'+'up'='CUP'

Can you help me to learn more?

(Other definitions for cup that I've seen before include "Trophy, drink" , "Trophy; drinking vessel" , "McCarthy, Walker or Maguire" , "Container to drink from - prize" , "Prize; vessel" .)

I've seen this clue in the Evening Standard.

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