The most common and most likely answer to this crossword clue is the 7 letter word BELATED
I've seen this crossword clue in The Guardian
B
E
L
A
T
E
D
More clues leading to the result BELATED
Buddy explains!

The straight part
We know that "overdue" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case overdue = belated.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 BELATED mean?
BELATED verb- To retard; cause something to be late; delay; benight.
- Later in relation to the proper time something should have happened.