The most common and most likely answer to this crossword clue is the 5 letter word ROMEO
I've seen this crossword clue in The Times
R
O
M
E
O
More clues leading to the result ROMEO
- Lover runs rings around yours truly
- Lover’s letter read out
- Young lover runs rings around me
- Great lover, antipodean native hugging me
- Shakespearean hero with capital O
- Capital O that signifies R
- Capital outlay initially required to make Don Juan?
- Lover boy making yours truly wear jumper
- Capital city with love for great lover
- Lover ultimately may be represented thus?
Buddy explains!

The straight part
We know that "Great lover" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case great lover = romeo.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.