Late last month began extramarital affair secretly with journalist (8)
I believe the answer is:
deceased
'late' is the definition.
(I've seen this before)
'last month began extramarital affair secretly with journalist' is the wordplay.
'last month' becomes 'dec' (December, last month of the year).
'began' indicates taking the first letters (I've seen 'begin' mean this).
'with' is a charade indicator (letters next to each other).
'journalist' becomes 'ed' (short for editor).
The first letters of 'extramarital affair secretly' is 'eas'.
'dec'+'eas'+'ed'='DECEASED'
(Other definitions for deceased that I've seen before include "departed" , "Passed away" , "Defunct" , "No longer living" , "Totally bereft of life" .)