Running right into relative — good (8)
I believe the answer is:
coursing
'running' is the definition.
('course' can be a synonym of 'run')
'right into relative good' is the wordplay.
'right' becomes 'r' (common abbreviation).
'into' means one lot of letters goes inside another.
'relative' becomes 'cousin' (cousin is a kind of relative).
'good' becomes 'g' (abbreviation).
'r' put into 'cousin' is 'coursin'.
'coursin'+'g'='COURSING'
(Other definitions for coursing that I've seen before include "Running" , "it can be fatal for hares" , "illegal hunting?" , "blood sport" , "Hunting with dogs" .)