Some object, nag or rant about being conceited (8)
I believe the answer is:
arrogant
'conceited' is the definition.
(thesaurus)
'some object nag or rant about' is the wordplay.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'about' shows that the letters should be reversed in order.
'tnagorra' is hidden in the letters of 'object nag or rant'.
'tnagorra' in reverse letter order is 'ARROGANT'.
'being' is the link.
(Other definitions for arrogant that I've seen before include "Overweening" , "Overbearing with exaggerated sense of superiority" , "Overly self-important" , "Having an exaggerated sense of one's own importance" , "Public speaker" .)