Inheritance finally claimed by particular relative (5)
I believe the answer is:
niece
'relative' is the definition.
(type of relative)
'inheritance finally claimed by particular' is the wordplay.
'finally' suggests the final letters.
'claimed by' means one lot of letters goes inside another.
'particular' becomes 'nice' (nice can mean particular or precise).
The final letter of 'inheritance' is 'e'.
'e' placed within 'nice' is 'NIECE'.
(Other definitions for niece that I've seen before include "A sibling's daughter" , "Brother or sister's daughter" , "Criminal" , "Kinswoman" , "Daughter of a sibling" .)