As before, run after the animal (8)
I believe the answer is:
antelope
'the animal' is the definition.
(I've seen this before)
'as before run' is the wordplay.
'as before' becomes 'ante' (I can't justify this - if you can you should give a lot more credence to this answer).
'run' becomes 'lope' (loping is a kind of running).
'ante'+'lope'='ANTELOPE'
'after' acts as a link.
Can you help me to learn more?
(Other definitions for antelope that I've seen before include "bounder!" , "grazing animal" , "Long-legged ruminant" , "Horned ruminant" , "Springboks, say" .)