Describe coming across the fourth cousin perhaps (8)
I believe the answer is:
relative
'cousin perhaps' is the definition.
(cousin is a kind of relative)
'describe coming across the fourth' is the wordplay.
'describe' becomes 'relate' (I've seen this in another clue).
'coming across' indicates putting letters inside.
'the fourth' becomes 'iv' (Roman numerals for four).
'relate' placed around 'iv' is 'RELATIVE'.
(Other definitions for relative that I've seen before include "one in a family" , "Blood connection is not absolute" , "Person related by blood or marriage" , "uncle, perhaps" , "Granny, perhaps" .)