The most common and most likely answer to this crossword clue is the 5 plus 7 letter word THROE (OTHER)
T
H
R
O
E
(
O
T
H
E
R
)
Buddy explains!

The straight part
We know that "Old poet’s probably left" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old poet’s probably left = throe (other).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.