Nanny yours truly’s rushed back to assist (9)

I believe the answer is:

nursemaid

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'nanny' is the definition.
(synonyms)

'yours truly's rushed back to assist' is the wordplay.
'yours truly's' becomes 'me's'.
'rushed' becomes 'run' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'back' says the letters should be written in reverse.
'to assist' becomes 'aid' (synonyms).
'mes'+'run'='mesrun'
'mesrun' backwards is 'nursem'.
'nursem'+'aid'='NURSEMAID'

Can you help me to learn more?

(Other definitions for nursemaid that I've seen before include "She may attend to babe" , "female carer" , "Alice, for example" , "caretaker" , "her charges are small" .)

I've seen this clue in The Times.

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