The most common and most likely answer to this crossword clue is the 8 letter word POSTDATE
I've seen this crossword clue in Independent
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The straight part
We know that "Possibly mark payment for next month" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case possibly mark payment for next month = postdate.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does POSTDATE mean?
POSTDATE noun- A date on a document later than the real date on which it was written.
- To occur after an event or time; to exist later on in time
- To assign an effective date to a document or action later than the actual date
- To affix a date to after the event.
- Postdated; made or done after the date assigned.