The most common and most likely answer to this crossword clue is the 6 letter word YAWNED
I've seen this crossword clue in The Times
Y
A
W
N
E
D
Buddy explains!

The straight part
We know that "looked bored" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case looked bored = yawned.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.
What does YAWNED mean?
YAWNED verb- To open the mouth widely and take a long, rather deep breath, often because one is tired or bored, and sometimes accompanied by pandiculation.
- To say while yawning.
- To present a wide opening.
- To open the mouth, or to gape, through surprise or bewilderment.
- To be eager; to desire to swallow anything; to express desire by yawning.