Thought Everyman and deejay regularly falling out (4)
I believe the answer is:
idea
'thought' is the definition.
(I know that thought can be written as idea)
'everyman and deejay regularly falling out' is the wordplay.
'everyman' becomes 'i' (where the crossword setter is 'Everyman').
'and' says to put letters next to each other.
'regularly falling out' indicates alternate letters.
The alternating letters of 'deejay' are 'dea'.
'i'+'dea'='IDEA'
(Other definitions for idea that I've seen before include "Purpose" , "Sudden inspiration?" , "Light bulb above head" , "Mental impression" , "Suggestion" .)