The most common and most likely answer to this crossword clue is the 8 letter word ROYALIST
I've seen this crossword clue in The Guardian
R
O
Y
A
L
I
S
T
More clues leading to the result ROYALIST
- Cavalier is solitary, abandoned
- Do solitary? Her Majesty’s pleasure for this one?
- ‘Roger Taylor is inside’
- ‘Hattersley with an agenda’? Not how you’d describe Corbyn
- Cavalier Rovers player? Top celeb
- Fan of Elizabeth Taylor is eccentric
- Potentially solitary 16-21
- Solitary oddball in opposition to the Republic?
- Cavalier king beheaded stalwart supporter
- Cavalier attitude’s beginning with Liberal in story, I suspect
Buddy explains!

The straight part
We know that "Fan of Elizabeth" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fan of elizabeth = royalist.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 ROYALIST mean?
ROYALIST noun- A monarchist (supporter of monarchy) or supporter of a particular royal régime.
- A legitimist, a supporter of a particular royal line, especially one in danger of being dispossessed of a throne or actually dispossessed of such, and claiming to have the better claim to the throne on the basis of line of descent; especially: