"The girl who was standing at the gate yesterday is my sister." "was" is needed because the girl stood at the gate yesterday - past tense. "is my sister" is correct because the girl at the gate is currently the speaker's sister. The meaning is not difficult. Apparently the speaker and the one being spoken to remember that yesterday they both saw a girl standing at the gate. The speaker has identified her as his sister.

I think you should use "was" instead of "is". Because the girl stood at the gate in past time.

you can also say: the girl standing at the gate yesterday, was my sister

You can also say, the girl who stood at the gate yesterday is my sister.