Beat that made Pilate apt to do the twist (9)

I believe the answer is:

palpitate

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'beat' is the definition.
(I know that palpitate is a more specific form of the action beat)

'made pilate apt to do the twist' is the wordplay.
'pilate apt' can be anagrammed to 'PALPITATE'.
But, I'm not sure how this is indicated.

'that' acts as a link.

Can you help me to learn more?

(Other definitions for palpitate that I've seen before include "Shake, tremble" , "Rapidly beat" , "quake" , "Beat abnormally quickly" , "flutter" .)

I've seen this clue in The Globe and Mail.

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