Artist Damien on time to show desire (6)
I believe the answer is:
thirst
'desire' is the definition.
(thirsting is a kind of desiring)
'artist damien on time' is the wordplay.
I cannot quite see 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 located in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
'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" .)