The most common and most likely answer to this crossword clue is the 4 letter word AJAR
I've seen this crossword clue in The Times
A
J
A
R
More clues leading to the result AJAR
Buddy explains!

The straight part
We know that "Partly open" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case partly open = ajar.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 AJAR mean?
AJAR verb- To turn or open slightly; to become ajar or to cause to become ajar; to be or to hang ajar.
- Slightly turned or opened.
- Slightly turned or opened.
- To show variance or contradiction with something; to be or cause to be askew.
- Out of harmony.
- Being at variance or in contradiction to something.