The most common and most likely answer to this crossword clue is the 4 letter word TATE
I've seen this crossword clue in The Guardian
T
A
T
E
More clues leading to the result TATE
- Popular spot for a hanging?
- Shabby articles by English gallery
- Rubbish English gallery
- Philanthropist‘s thank-you note
- Tense worried comedian
- Thank you note for collection of pictures
- Art gallery‘s thank-you note
- Going around French State Gallery
- Irish poet contributing to event at Easter
- British art institution, say, a non-starter
Buddy explains!

The straight part
We know that "Gallery" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gallery = tate.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.