Sickly looking boy, but in demand (6)
I believe the answer is:
wanted
'in demand' is the definition.
(I've seen this in another clue)
'sickly looking boy' is the wordplay.
'sickly looking' becomes 'wan' (I've seen this in another clue).
'boy' becomes 'ted' (short for Edward or Theodore).
'wan'+'ted'='WANTED'
'but' acts as a link.
(Other definitions for wanted that I've seen before include "sought by police?" , "Desired or wished for" , "Wished-for" , "Lacked; type of police poster" , "Desired by police?" .)