The most common and most likely answer to this crossword clue is the 8 letter word HARRISON
I've seen this crossword clue in Financial Times
H
A
R
R
I
S
O
N
More clues leading to the result HARRISON
- Member of Shadows performing as member of Beatles
- Ford salesman’s negative reply – breathe evenly turning it all over
- President’s rash iron shot
- Tailless nag is acceptable for clockmaker
- Guitarist mostly difficult — definitely not coming back
- A bishop is performing at back of hotel as member of a group
- Guitarist‘s fantastic writing harmonies without me
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 = harrison.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.