Drawer describing artist as 'more eager' (9)
I believe the answer is:
'more eager' is the definition.
(thirsty can mean eager or keen)
'drawer describing artist' is the wordplay.
'drawer' becomes 'tier' (tie can mean to draw in sports).
'describing' is an insertion indicator (describe can mean to form the outline of).
'artist' becomes 'Hirst' (artist Damien Hirst).
'tier' placed around 'hirst' is 'THIRSTIER'.
'as' acts as a link.
(Another definition for thirstier that I've seen is " needing more water".)