Run from the initial rubbish (4)
I believe the answer is:
trot
'run' is the definition.
(trot is a kind of run)
'the initial rubbish' is the wordplay.
'initial' indicates taking the first letters.
'rubbish' becomes 'rot' (both can mean nonsense).
The initial letter of 'the' is 't'.
't'+'rot'='TROT'
'from' is the link.
(Other definitions for trot that I've seen before include "Go or walk briskly" , "Follower of revolutionary" , "Moderate running pace" , "moderate movement" , "Fairly brisk pace" .)