Long time associated with a YBA (6)
I believe the answer is:
thirst
'long' is the definition.
(thirst can mean to long or yearn for something)
'time associated with a yba' is the wordplay.
'time' becomes 't' (abbreviation).
'associated with' means one lot of letters go next to another.
'a yba' becomes 'Hirst' (Young British Artist Damien Hirst).
't'+'hirst'='THIRST'
(Other definitions for thirst that I've seen before include "Strong desire for something" , "Longing" , "Long" , "Hunger" , "A craving for drink or knowledge" .)