The most common and most likely answer to this crossword clue is the 5 letter word KOALA
I've seen this crossword clue in Financial Times
K
O
A
L
A
More clues leading to the result KOALA
- Put out a note for Aussie tree-climber
- Tree-hugger fine about hugging a laurel finally
- Marsupial known at first over a large area
- Unfortunately knocked back, taking oxygen for cold — am I up a gum tree?
- Kind of nut inspiring a marsupial
- Knock out in the manner of French marsupial
- Floor in the style of Oz native
- Lover of eucalyptus stunning a large area
- Fine boomerangs, in the style of a native Australian
- Bear a left, then a right, then reverse
Buddy explains!

The straight part
We know that "Lover of eucalyptus" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lover of eucalyptus = koala.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 KOALA mean?
KOALA noun- A tree-dwelling marsupial, Phascolarctos cinereus, that resembles a small bear with a broad head, large ears and sharp claws, mainly found in eastern Australia.