Question

Cats, on the other hand, are very calm; they don’t tend to say much unless (there, their, they’re) hungry or accidentally stepped on.

Answer 1

Answer: they're

Explanation: They're because they're is a form of they are. If you put that in a sentence, it becomes:

Cats, on the other hand, are very calm; they don’t tend to say much unless they are hungry or accidentally stepped on.

Answer 2

Answer:

they're

Explanation:

there signifies a place (there is a blue house)

their signifies something that is a possession (their house is blue)

they're is "they are" so (they are cats)