Leader described by prominent journalist as 'conceited' (9)
I believe the answer is:
bigheaded
'conceited' is the definition.
(bigheaded can mean conceited or arrogant)
'leader described by prominent journalist' is the wordplay.
'leader' becomes 'head' (head is a kind of leader).
'described by' means one lot of letters goes inside another (to describe can mean to form an outline).
'prominent' becomes 'big' (synonyms).
'journalist' becomes 'ed' (short for editor).
'big'+'ed'='biged'
'head' placed into 'biged' is 'BIGHEADED'.
'as' acts as a link.
(Another definition for bigheaded that I've seen is " Conceited with large cranium".)