The most common and most likely answer to this crossword clue is the 3 plus 6 letter word TEA GARDEN
I've seen this crossword clue in The Times
T
E
A
G
A
R
D
E
N
More clues leading to the result TEA GARDEN
- Trail round English forest leading to open-air eatery
- Great Dane let loose in open-air restaurant
- Great Dane running around place for outdoor refreshments
- Grandee at fancy restaurant in the open air
- Trombonist's eatery in the Open
- . Broken gate leads to forest and al fresco cafe
- Grade neat new restaurant
- New gate leading to forest that offers outdoor refreshments
- Refreshing place, Newgate Forest
- Jelly and custard ultimately polished off by youth in outdoor cafe
Buddy explains!

The straight part
We know that "restaurant in the open air" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case restaurant in the open air = tea garden.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.