Sect missing the first of last month in brief (3)
I believe the answer is:
ult
'last month in brief' is the definition.
(abbreviation meaning last month)
'sect missing the first' is the wordplay.
'sect' becomes 'cult' (I've seen this before).
'missing the first' means to remove the first letter.
'cult' with its initial letter removed is 'ULT'.
'of' acts as a link.
(Other definitions for ult that I've seen before include "In brief, notation for last month" , "In short, last month" , "Notation in business correspondence meaning last month" , "Of the month preceding the present one, in short" , "Abbreviation in correspondence for last month" .)