Gets faster in rush to drink (6,2)

I believe the answer is:

speeds up

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

'rush to drink' is the wordplay.
'rush' becomes 'speed' (synonyms).
'to drink' becomes 'sup' (to sup is to drink).
'speed'+'sup'='SPEEDS UP'

'in' is the link.

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

I've seen this clue in The Sun.

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