Present lady’s coat in a gentle way (8)

I believe the answer is:

tenderly

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'in a gentle way' is the definition.
I can't judge whether this defines the answer.

'present lady's coat' is the wordplay.
'present' becomes 'tender' (tendering is a kind of presenting).
'coat' suggests removing the centre (only the letters which coat the word are used).
'lady' with its middle removed is 'ly'.
'tender'+'ly'='TENDERLY'

Can you help me to learn more?

(Other definitions for tenderly that I've seen before include "in affectionate manner" , "In gentle and loving manner" , "Sensitively" , "Gently, sympathetically" , "in caring way" .)

I've seen this clue in The Times.

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