Reportedly run from insect (4)
I believe the answer is:
flea
'insect' is the definition.
(I know that flea is a type of insect)
'reportedly run' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'run' becomes 'flee' (to flee is to run away).
'flee' is a homophone of 'FLEA'.
'from' acts as a link.
(Other definitions for flea that I've seen before include "Circus insect?" , "high-jumper" , "In your ear, this insect is a rebuke" , "Blood-sucking parasites" , "Biting type" .)