Can we use simple past and present simple tense in single sentence?

I'm writing a short story. I will work with native speakers to get my work edited in near future. Before that, I want to make sure that I write the story as grammatically accurate as possible.

The story is being written in simple past tense. It is a third person narrative.

A sentence in my story reads, "He asked the woman to wait in the lobby until a program manager meets her."

Is the above sentence in the quotes grammatically correct?