Reportedly follow story (4)
I believe the answer is:
tale
'story' is the definition.
(I know that story can be written as tale)
'reportedly follow' is the wordplay.
'reportedly' shows a homophone (sound like).
'follow' becomes 'tail' (both can mean to chase or pursue).
'tail' sounds like 'TALE'.
(Other definitions for tale that I've seen before include "Old wives' recital?" , "See 12" , "Report" , "relation" , "Yarn or story" .)