The most common and most likely answer to this crossword clue is the 8 letter word LADYSHIP
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More clues leading to the result LADYSHIP
Buddy explains!

The straight part
We know that "Her Majesty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case her majesty = ladyship.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 LADYSHIP mean?
LADYSHIP noun- Term of respect for a woman of the peerage without using her title.
- (English and Commonwealth) Formal form of address for a lady judge (as opposed to the informal "judge").