Subtle, absorbing end of tale one's related (5)
I believe the answer is:
niece
'one's related' is the definition.
(niece is a type of relative)
'subtle absorbing end of tale' is the wordplay.
'subtle' becomes 'nice' (nice can mean subtle or precise).
'absorbing' means one lot of letters goes inside another.
'end of' suggests the final letters.
The last letter of 'tale' is 'e'.
'nice' enclosing 'e' is 'NIECE'.
(Other definitions for niece that I've seen before include "Young female relative" , "A sibling's child" , "girl further down the line" , "[PRIEST'S] daughter?" , "Criminal" .)