The most common and most likely answer to this crossword clue is the 4 letter word WORN
I've seen this crossword clue in The Daily Telegraph
W
O
R
N
Buddy explains!
The straight part
We know that "Exhausted" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case exhausted = worn.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 WORN mean?
WORN verb- To carry or have equipped on or about one's body, as an item of clothing, equipment, decoration, etc.
- To have or carry on one's person habitually, consistently; or, to maintain in a particular fashion or manner.
- To bear or display in one's aspect or appearance.
- (with "it") To overcome one's reluctance and endure a (previously specified) situation.
- To eat away at, erode, diminish, or consume gradually; to cause a gradual deterioration in; to produce (some change) through attrition, exposure, or constant use.
- To undergo gradual deterioration; become impaired; be reduced or consumed gradually due to any continued process, activity, or use.
- To exhaust, fatigue, expend, or weary.
- To last or remain durable under hard use or over time; to retain usefulness, value, or desirable qualities under any continued strain or long period of time; sometimes said of a person, regarding the quality of being easy or difficult to tolerate.
- (in the phrase "wearing on (someone)") To cause annoyance, irritation, fatigue, or weariness near the point of an exhaustion of patience.
- (of time) To pass slowly, gradually or tediously.
- To bring (a sailing vessel) onto the other tack by bringing the wind around the stern (as opposed to tacking when the wind is brought around the bow); to come round on another tack by turning away from the wind. Also written "ware". Past: weared, or wore/worn.
- To guard; watch; keep watch, especially from entry or invasion.
- To defend; protect.
- To ward off; prevent from approaching or entering; drive off; repel.
- To conduct or guide with care or caution, as into a fold or place of safety.
- Damaged and shabby as a result of much use