The most common and most likely answer to this crossword clue is the 6 letter word MORROW
M
O
R
R
O
W
Buddy explains!
The straight part
We know that "the following day" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the following day = morrow.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 MORROW mean?
MORROW noun- The next or following day.
- Morning.
- To dawn