The most common and most likely answer to this crossword clue is the 4 letter word YAWN
I've seen this crossword clue in The Guardian
Y
A
W
N
More clues leading to the result YAWN
- Your audience will not initially sound bored
- New style recalled something dull
- New method to get over a boring person
- Baby finally, by daybreak, dropping head to show sign of tiredness
- Boring person with new style, in retrospect
- Boring event? New approach must come about
- Veer to north and look ready for bed
- Sign of boredom? New approach backfired
- Be open-mouthed as new fashion gets taken up
- Open up North Street from below
Buddy explains!

The straight part
We know that "sign of tiredness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sign of tiredness = yawn.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 YAWN mean?
YAWN noun- The action of yawning; opening the mouth widely and taking a long, rather deep breath, often because one is tired or bored.
- A particularly boring event.
- 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.