Wondering why my new bathroom sink does not have an overflow hole that I could see in my old sink/

Did you just purchase a new home? If so, it could be that the contractor chose a "cheaper" sink model. Most sinks do have overflow openings. It's just the cheaper sinks that don't have it.

The Twink nailed it.
Some of the newer lavatories have no overflow just like a vessel sink. I'm curious, what type of drain came with it. Tom

Christine, I do not believe it is necessarily a "cheap" sink. As Tom said, newer sinks do not have overflow. These sinks usually are designer's , expensive sinks. Usually, these sinks come from foreign countries, like from Europe or Japan. You can also see them in Ikea.

In my area, it is a Code. Every sink ( and tub ) has to have overflow.