The most common and most likely answer to this crossword clue is the 7 plus 3 plus 4 letter word GETTING ONE DOWN
I've seen this crossword clue in The Times
G
E
T
T
I
N
G
O
N
E
D
O
W
N
Buddy explains!
The straight part
We know that "Wearying" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wearying = getting one down.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.