Drop off returning ex-PM, drunk after drive (2,2,5)

I believe the answer is:

go to sleep

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'drop off' is the definition.
(synonyms)

'returning ex-pm drunk after drive' is the wordplay.
I cannot really see how this works, but
'drive' could be 'go' (I've seen this in other clues) and 'go' is present in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for go to sleep that I've seen before include "Drop off" , "Lose consciousness" .)

I've seen this clue in The Telegraph.

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