Relative with endless string ... (4)
I believe the answer is:
twin
'relative' is the definition.
(twin is a kind of relative)
'endless string' is the wordplay.
'endless' means to remove the last letter.
'string' becomes 'twine' ('twine' can be a synonym of 'string').
'twine' with its final letter taken away is 'TWIN'.
'with' is the link.
(Other definitions for twin that I've seen before include "indistinguishable from the next?" , "One of an identical pair" , "Family member" , "Castor or Pollux?" , "One of two conceived simultaneously" .)