Ran south and ran off (8)
I believe the answer is:
sprinted
'ran' is the definition.
(sprinting is a kind of running)
'south and ran off' is the wordplay.
'south' becomes 'S' (abbreviation).
'and' means one lot of letters go next to another.
'ran off' becomes 'printed' (I've seen this in another clue).
's'+'printed'='SPRINTED'
(Other definitions for sprinted that I've seen before include "Raced at full speed" , "Ran as fast as possible" , "moved very quickly" , "Ran at full speed over short distance" .)