Kate’s unusual interest (5)
I believe the answer is:
stake
'interest' is the definition.
('stake' can be a synonym of 'interest')
'kate's unusual' is the wordplay.
'unusual' indicates an anagram.
'kates' anagrammed gives 'STAKE'.
(Other definitions for stake that I've seen before include "Money gambled" , "Financial interest" , "The money risked on a gamble" , "Pale" , "that's used in punt" .)