I'll fly round - only too happy to (7)

I believe the answer is:

willing

I'm a little stuck... Click here to teach me more about this clue!

'only too happy to' is the definition.
I can't judge whether this definition defines the answer.

'i'll fly round' is the wordplay.
'fly' becomes 'wing' (synonyms).
'round' is an insertion indicator.
'ill' going within 'wing' is 'WILLING'.

Can you help me to learn more?

(Other definitions for willing that I've seen before include "game?" , "Ready and eager" , "Ready and keen" , "Compliant" , "Amenable, consenting" .)

I've seen this clue in the Evening Standard.

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