Writer’s project regularly displayed (4)
I believe the answer is:
poet
'writer's' is the definition.
(poet is a kind of writer)
'project regularly displayed' is the wordplay.
'regularly displayed' means one should take alternating letters (letters selected on a regular basis).
The alternate letters of 'project' are 'POET'.
(Other definitions for poet that I've seen before include "Bard" , "Eg, Keats or Auden" , "author" , "Pound, say" , "Rhymer" .)