The most common and most likely answer to this crossword clue is the 10 letter word RIGHT-HAND
I've seen this crossword clue in Financial Times
R
I
G
H
T
-
H
A
N
D
More clues leading to the result RIGHT-HAND
Buddy explains!

The straight part
We know that "This man is deputy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case this man is deputy = right-hand.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 RIGHT-HAND mean?
RIGHT-HAND adjective- Of, relating to, or located on the right
- Designed for use by the right hand
- In the direction or orientation to the right-hand rule (a right-hand thread)