In short supply (6)
(Other definitions for sparse that I've seen before include "Rare" , "Thinly dotted about" , "One's not at all thick" , "rarely occurring" , "Thin on the ground, scarce" .)
'in short supply' is the definition.
(both can mean rare)
This is all the clue.
(Other definitions for scarce that I've seen before include "Not enough to meet demand" , "Hard to obtain" , "Not plentiful, in short supply" , "Rare shock Conservative getting in" , "Common? Definitely not" .)