The most common and most likely answer to this crossword clue is the 8 letter word WORTHILY
I've seen this crossword clue in The Sunday Telegraph
W
O
R
T
H
I
L
Y
More clues leading to the result WORTHILY
Buddy explains!

The straight part
We know that "In virtuous way" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in virtuous way = worthily.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.