The most common and most likely answer to this crossword clue is the 9 letter word PLEASANCE
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More clues leading to the result PLEASANCE
Buddy explains!

The straight part
We know that "Part of garden" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of garden = pleasance.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 PLEASANCE mean?
PLEASANCE noun- Willingness to please, or the action of pleasing; courtesy.
- The feeling of being pleased; pleasure, delight.
- Grounds laid out with shady walks, trees and shrubs, statuary, and ornamental water; a secluded part of a garden.