Crossword Genius

Prompt to follow Conservative Party (7)

Ross

I believe the answer is:

carouse

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

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

'prompt to follow conservative' is the wordplay.
I cannot quite understand how this works, but
'conservative' could be 'c' (UK political abbreviation) and 'c' is found within the answer.
The remaining letters 'arouse' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for carouse that I've seen before include "Engage in boisterous, drunken merry-making" , "Celebrate noisily" , "Party noisily" , "booze" , "Take a course to party wildly" .)

I've seen this clue in The Times.
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