Firm up on time of month, briefly (3)
I believe the answer is:
oct
'month briefly' is the definition.
(abbreviation for October; 'briefly' asks for an abbreviation)
'firm up on time' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'on' says to put letters next to each other.
'time' becomes 't' (abbreviation).
'co' reversed gives 'oc'.
'oc'+'t'='OCT'
'of' acts as a link.
(Other definitions for oct that I've seen before include "Month, in short" , "10th month (abbrev.)" .)