The most common and most likely answer to this crossword clue is the 7 plus 1 letter word GISCARD D
G
I
S
C
A
R
D
D
Buddy explains!
The straight part
We know that "president of yesteryear" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case president of yesteryear = giscard d.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.