The most common and most likely answer to this crossword clue is the 8 plus 5 letter word DONKEY’S YEARS
I've seen this crossword clue in The Guardian
D
O
N
K
E
Y
â
€
™
S
Y
E
A
R
S
Buddy explains!

The straight part
We know that "a long time" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a long time = donkey’s years.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.