Swayed right away in discussion that went to one's head? (6,3)
I believe the answer is:
cocked hat
'that went to one's head?' is the definition.
(historical type of hat)
'swayed right away in discussion' is the wordplay.
'swayed' becomes 'rocked' ('rock' can be a synonym of 'sway').
'right' becomes 'r' (common abbreviation).
'away' indicates named letters should be taken away.
'in' indicates putting letters inside.
'discussion' becomes 'chat'.
'rocked' with 'r' taken away is 'ocked'.
'ocked' going inside 'chat' is 'COCKED HAT'.
(Other definitions for cocked hat that I've seen before include "Military cover" , "one may knock into" , "Triangular headgear, pointed at front and back" , "capital investment" .)