Heidegger's regularly showing irritation (4)
I believe the answer is:
edge
'irritation' is the definition.
(on edge can mean irritated)
'heidegger's regularly' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternating letters of 'heidegger' are 'EDGE'.
'showing' acts as a link.
(Other definitions for edge that I've seen before include "Rim, lip" , "Snick - boundary" , "Border - meeting place" , "Guitarist with U2" , "Move carefully; limit" .)