I'm going to manage in style (8)
I believe the answer is:
'i'm going' is the definition.
('I'm going' can mean 'I'm leaving')
'manage in style' is the wordplay.
'manage' becomes 'fare' (how you fare is how you manage with something).
'in style' becomes 'well' (in style can mean well or in an impressive way).
'to' acts as a link.
(Other definitions for farewell that I've seen before include "Goodbye, cheerio" , "Valediction" , "Wish on leave-taking" , "Cape at the southernmost point of Greenland" , "Say goodbye" .)