Make him care about an idle fancy (7)
I believe the answer is:
chimera
'an idle fancy' is the definition.
(chimera can mean a fancy or delusion)
'make him care' is the wordplay.
'make' indicates anagramming the letters.
'him'+'care'='himcare'
'himcare' is an anagram of 'CHIMERA'.
'about' acts as a link.
(Other definitions for chimera that I've seen before include "fantasy" , "Vain, foolish, or incongruous fancy" , "Mythological animal; something illusory" , "Creature such as a gryphon" , "Mythological monster" .)