The most common and most likely answer to this crossword clue is the 11 letter word MERITORIOUS
I've seen this crossword clue in The Times
M
E
R
I
T
O
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I
O
U
S
Buddy explains!

The straight part
We know that "Deserving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deserving = meritorious.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 MERITORIOUS mean?
MERITORIOUS adjective- Deserving of merit or commendation; deserving reward.