The most common and most likely answer to this crossword clue is the 10 plus 3 letter word MIDSUMMERS DAY
I've seen this crossword clue in The Times
M
I
D
S
U
M
M
E
R
S
D
A
Y
Buddy explains!
The straight part
We know that "when periodic payments due" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case when periodic payments due = midsummers day.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.