The most common and most likely answer to this crossword clue is the 11 letter word BLEARY-EYED
I've seen this crossword clue in Independent
B
L
E
A
R
Y
-
E
Y
E
D
More clues leading to the result BLEARY-EYED
Buddy explains!
The straight part
We know that "tired-looking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tired-looking = bleary-eyed.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.