One who's desperate kicks the bucket and swells (7)
I believe the answer is:
dandies
'swells' is the definition.
('dandy' can be a synonym of 'swell')
'one who's desperate kicks the bucket' is the wordplay.
'one who's desperate' becomes 'dan' (comic book character Desperate Dan).
'kicks the bucket' becomes 'dies' (kick the bucket can informally mean to die).
'dan'+'dies'='DANDIES'
'and' acts as a link.
(Other definitions for dandies that I've seen before include "bucks" , "Smartly dressed fellows like Beau Brummel" , "Men who pay excessive attention to their clothes" , "Men who over-dress, like Beau Brummel" , "men about town" .)