The most common and most likely answer to this crossword clue is the 4 letter word PALL
I've seen this crossword clue in The Times
P
A
L
L
More clues leading to the result PALL
- Become tedious letter-writer, by the sound of it?
- Athena, as concealed in shadow
- Does one hold up one who is late?
- Weary? Get a blanket
- Friend at length is to become tedious
- Mall forerunner’s become tiresome
- Dark covering another setter while speaking
- Support given by everyone to both halves of afternoon game
- Weary old man’s put on pounds
- Principal lamenter may be seen as such
Buddy explains!

The straight part
We know that "Weary/a blanket" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weary/a blanket = pall.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 PALL mean?
PALL noun- Senses relating to cloth.
- Senses relating to clothing.
- To cloak or cover with, or as if with, a pall.
- To make vapid or insipid; to make lifeless or spiritless; to dull, to weaken.
- To become dull, insipid, tasteless, or vapid; to lose life, spirit, strength, or taste.
- A feeling of nausea caused by disgust or overindulgence.