The most common and most likely answer to this crossword clue is the 8 letter word CHAIRMEN
I've seen this crossword clue in The Times
C
H
A
I
R
M
E
N
More clues leading to the result CHAIRMEN
Buddy explains!
The straight part
We know that "Presidents" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case presidents = chairmen.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 CHAIRMEN mean?
CHAIRMEN noun- A person presiding over a meeting.
- The head of a corporate or governmental board of directors, a committee, or other formal entity.
- Someone whose job is to carry people in a portable chair, sedan chair, or similar conveyance.