The most common and most likely answer to this crossword clue is the 8 letter word DRAINING
I've seen this crossword clue in The Daily Telegraph
D
R
A
I
N
I
N
G
Buddy explains!

The straight part
We know that "Wearisome" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wearisome = draining.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 DRAINING mean?
DRAINING verb- To lose liquid.
- To flow gradually.
- To cause liquid to flow out of.
- To convert a perennially wet place into a dry one.
- To deplete of energy or resources.
- To draw off by degrees; to cause to flow gradually out or off; hence, to exhaust.
- To filter.
- To fall off the bottom of the playfield.
- The practice of exploring drains, tunnels, or sewers.
- The process by which something is drained or emptied.
- (usually in the plural) The liquid drained from something.
- That drains.