Argued with a flier, indeed (7)
I believe the answer is:
debated
'argued' is the definition.
('debate' can be a synonym of 'argue')
'a flier indeed' is the wordplay.
I cannot quite understand how this works, but
'a' is found in the answer.
The remaining letters 'debted' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'with' is the link.
Can you help me to learn more?
(Other definitions for debated that I've seen before include "Shared opinions" , "Argued" , "Considered" , "Contemplated" , "Discussed in public" .)