On the sly perhaps but in a sincere way (8)

I believe the answer is:

honestly

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'in a sincere way' is the definition.
I can't tell whether this defines the answer.

'on the sly perhaps' is the wordplay.
'perhaps' indicates an anagram.
'on'+'the'+'sly'='onthesly'
'onthesly' with letters rearranged gives 'HONESTLY'.

'but' acts as a link.

Can you help me to learn more?

(Other definitions for honestly that I've seen before include "In a truthful way" , "In a fair-dealing way" , "Really; truthfully" , "How law-abiding people act" , "No kidding!" .)

I've seen this clue in The Globe and Mail.

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