Top tennis player, holding soft drink, steps on it (6,2)

I believe the answer is:

speeds up

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'steps on it' is the definition.
Although both the answer and definition are verbs in their -s form, I can't understand how one could define the other.

'top tennis player holding soft drink' is the wordplay.
'top tennis player' becomes 'seed' (a seeded player).
'holding' indicates putting letters inside.
'soft' becomes 'p' (musical abbreviation for 'piano').
'drink' becomes 'sup' (to sup is to drink).
'seed' enclosing 'p' is 'speed'.
'speed'+'sup'='SPEEDS UP'

Can you help me to learn more?

(Other definitions for speeds up that I've seen before include "Gets faster" , "Accelerates" .)

I've seen this clue in The Guardian.

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