The most common and most likely answer to this crossword clue is the 7 letter word BANDBOX
I've seen this crossword clue in The Times
B
A
N
D
B
O
X
Buddy explains!

The straight part
We know that "container for hats" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case container for hats = bandbox.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 BANDBOX mean?
BANDBOX noun- A box of lightweight construction (e.g. cardboard, thin wood) for carrying hats or other apparel items.
- A small baseball park conducive to scoring home runs.