Go to seed, having originally served this old family member (8)
I believe the answer is:
stagnate
'go to seed' is the definition.
(thesaurus)
'originally served this old family member' is the wordplay.
'originally' indicates taking the first letters.
'old family member' becomes 'agnate' (family member in the male line).
The first letters of 'served this' is 'st'.
'st'+'agnate'='STAGNATE'
'having' is the link.
(Other definitions for stagnate that I've seen before include "Cease moving" , "Stop shifting" , "Become foul from inertia" , "(Of water) become motionless" , "Fester" .)