Artist Damien on time to show desire (6)
I believe the answer is:
thirst
'desire' is the definition.
(I know that thirst is a type of desire)
'artist damien on time' is the wordplay.
I cannot quite understand how this works, but
'artist' could be 'hirst' (artist Damien Hirst) and 'hirst' is found in the answer.
'time' could be 't' (abbreviation) and 't' is present in the answer.
No letters remain.
This explanation may well be incorrect...
'to show' acts as a link.
Can you help me to learn more?
(Other definitions for thirst that I've seen before include "T-shirt (anag)" , "lack of water" , "Longing" , "Strong desire from dehydration?" , "The inducement for 5 Down" .)