Being pretentious, started improving (6-2)
I believe the answer is:
jumped-up
'being pretentious' is the definition.
('jumped-up' can be similar in meaning to 'pretentious')
'started improving' is the wordplay.
'started' becomes 'jumped' (jumping is a kind of starting).
'improving' becomes 'up' ('up' can be a synonym of 'improving').
'jumped'+'up'='JUMPED-UP'
(Other definitions for jumped-up that I've seen before include "Of one who has suddenly and undeservedly risen in status" , "Considering oneself of a higher status?" , "High and mighty" , "Arrogant (having risen socially)" , "Arrogant, cocky" .)