The most common and most likely answer to this crossword clue is the 8 letter word MAESTOSO
I've seen this crossword clue in The Times
M
A
E
S
T
O
S
O
More clues leading to the result MAESTOSO
Buddy explains!

The straight part
We know that "regally" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case regally = maestoso.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 MAESTOSO mean?
MAESTOSO adverb- Majestically