Estate finally claimed by sweet relative (5)
I believe the answer is:
niece
'relative' is the definition.
(type of relative)
'estate finally claimed by sweet' is the wordplay.
'finally' says to take the final letters.
'claimed by' is an insertion indicator.
'sweet' becomes 'nice' (I've seen this in other clues).
The last letter of 'estate' is 'e'.
'e' going within 'nice' is 'NIECE'.
(Other definitions for niece that I've seen before include "One of the family" , "[PRIEST'S] daughter?" , "A younger female relative" , "A sibling's child" , "Criminal" .)