Crossword Genius

Don's turned over in bed (3,2)

Ross

I believe the answer is:

put on

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'don's' is the definition.
(synonyms)

'turned over in bed' is the wordplay.
I cannot quite understand how this works, but
'over' could be 'on' (physically on top of) and 'on' is present in the answer.
The remaining letters 'put' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for put on that I've seen before include "Donned" , "Assume < present" , "Increase as with weight" , "Don clothes or stage play" , "Apply (to a surface) - present (on stage)" .)

I've seen this clue in The Independent.
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