The most common and most likely answer to this crossword clue is the 7 plus 6 letter word WOODROW WILSON
I've seen this crossword clue in The Times
W
O
O
D
R
O
W
W
I
L
S
O
N
Buddy explains!
The straight part
We know that "US president" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case us president = woodrow wilson.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.