Read by custom on the first of December (7)
I believe the answer is:
perused
'read' is the definition.
(I've seen this before)
'by custom on the first of december' is the wordplay.
'by' becomes 'per' (I've seen this in another clue).
'custom' becomes 'use' (use is a kind of custom).
'on' is a charade indicator (letters next to each other).
'the first of december' becomes 'd' (pst letter of 'december').
'per'+'use'+'d'='PERUSED'
(Other definitions for perused that I've seen before include "Read (something) very carefully" , "Browsed" , "Studied" , "Scanned" .)