Long time with artist (6)
I believe the answer is:
thirst
'long' is the definition.
(thirst can mean to long or yearn for something)
'time with artist' is the wordplay.
'time' becomes 't' (abbreviation).
'with' means one lot of letters go next to another.
'artist' becomes 'Hirst' (artist Damien Hirst).
't'+'hirst'='THIRST'
(Other definitions for thirst that I've seen before include "Quaff to slake it" , "Want of drink" , "A craving for drink or knowledge" , "The inducement for 5 Down" , "Longing" .)