Taking care of Carol after getting run over (7)

I believe the answer is:

nursing

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'taking care' is the definition.
'nursing' can be an answer for 'care' (nursing is a kind of care). I'm not certain of the 'taking' bit.

'carol after getting run over' is the wordplay.
'carol' becomes 'sing' (I've seen this before).
'after getting' means one lot of letters go next to another.
'over' says the letters should be written backwards.
'run' reversed gives 'nur'.
'sing' after 'nur' is 'NURSING'.

'of' is the link.

Can you help me to learn more?

(Other definitions for nursing that I've seen before include "Caring career" , "Patient care" , "sister's career" , "Tending (patients)" , "Caring profession" .)

I've seen this clue in The Hindu.

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