Goddess left daughter in charge of arms (8)
I believe the answer is:
heraldic
'of arms' is the definition.
'goddess left daughter in charge' is the wordplay.
'goddess' becomes 'hera' (Greek goddess).
'left' becomes 'L' (common abbreviation).
'daughter' becomes 'd' (genealogical abbreviation).
'in charge' becomes 'ic' (abbreviation for 'in charge').
'hera'+'l'+'d'+'ic'='HERALDIC'
(Other definitions for heraldic that I've seen before include "related to genealogical study" , "Relating to officers who register genealogies" , "Of armorial bearings" , "Of family crests" , "Relating to coats of arms etc" .)