Feeling that makes one hang on? (8)
I believe the answer is:
hangover
'feeling' is the definition.
(I have seen 'Sick feeling' mean 'hangover' so perhaps 'feeling' could also mean 'hangover')
'one hang on?' is the wordplay.
'on?' becomes 'over' (I've seen this in other clues).
'hang'+'over'='HANGOVER'
'that makes' acts as a link.
(Other definitions for hangover that I've seen before include "Morning-after problem" , ""Morning after" experience" , "result of over-indulgence?" , "Effect of excess drink" , "a pain come the morning?" .)