The most common and most likely answer to this crossword clue is the 6 letter word ARBOUR
I've seen this crossword clue in The Daily Telegraph
A
R
B
O
U
R
Buddy explains!

The straight part
We know that "shady garden alcove" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shady garden alcove = arbour.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 ARBOUR mean?
ARBOUR noun- A shady sitting place, usually in a park or garden, and usually surrounded by climbing shrubs or vines and other vegetation.
- A shady walk.