Self-important (9)
(Other definitions for conceited that I've seen before include "Very proud of oneself" , "Arrogant" , "Swollen-headed" , "With a high opinion of oneself" , "Vain; narcissistic" .)
'self-important' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for uppity that I've seen before include "Cheeky or presumptuous" , "Not easily persuaded" , "Self-important, arrogant" , "Needing to be slapped down?" , "Pert; haughty" .)
'self-important' is the definition.
(synonyms)
This is the entire clue.
(Other definitions for arrogant that I've seen before include "Public speaker" , "Proud and contemptuous" , "Showing an offensive sense of superiority" , "High and mighty" , "Over-cocky" .)