The most common and most likely answer to this crossword clue is the 7 letter word RALEIGH
I've seen this crossword clue in The Daily Telegraph
R
A
L
E
I
G
H
More clues leading to the result RALEIGH
- Explorer mostly just consuming beer
- Courtier just wasting time drinking beer
- Explorer who is audible in mass meeting
- Hunt maybe led by artist and explorer
- Beer consumed by Doctor Who, essentially an adventurer
- Tobacco-importer briefly justified importing beer
- Elizabeth’s favourite beer in privilege curtailed
- Get better phoning old explorer
- Elizabeth I’s favourite beer in curtailed privilege
- What Cupid drew, heading off after artist and explorer
Buddy explains!

The straight part
We know that "one of Elizabeth’s favourites" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one of elizabeth’s favourites = raleigh.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.