The most common and most likely answer to this crossword clue is the 15 letter word HIGH-HANDEDNESS
I've seen this crossword clue in Financial Times
H
I
G
H
-
H
A
N
D
E
D
N
E
S
S
Buddy explains!
The straight part
We know that "imperious quality" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case imperious quality = high-handedness.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.