The most common and most likely answer to this crossword clue is the 4 plus 1 plus 7 letter word JOHN F KENNEDY
I've seen this crossword clue in The Guardian
J
O
H
N
F
K
E
N
N
E
D
Y
Buddy explains!
The straight part
We know that "President" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case president = john f kennedy.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.