"그녀는 코트를 갈아입어요."
Translation:She changes her coat.
It's implied. Since she is the topic, it's natural the coat is hers unless otherwise specified.
That sounds like an exchange at a store since you say "coats" -> 코트를 바꾸다
Doesn't 갈아입어요 imply that the lady takes one coat off and puts another one on? She doesn't change the one coat she is wearing, she is actually swapping coats, no?
I think so. According to NAVER dictionary, to change A for B is A를 B로 갈아입다. Now, without the 로 part, naturally I'd assume that the new piece of clothes she's putting on is also a coat.