The most common and most likely answer to this crossword clue is the 5 letter word TEDDY
I've seen this crossword clue in The Guardian
T
E
D
D
Y
Buddy explains!

The straight part
We know that "Bear" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bear = teddy.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 TEDDY mean?
TEDDY noun- By extension, any stuffed toy.
- A type of all-in-one piece of women's underwear.
- A plush toy in the shape of a bear.
- A lovable, endearing, large, strong, hairy, or sweet man