4 of 5 concusion

What is the proper protocol for applying to a postdoc sponsored by an one's undergraduate adviser?

I am finishing up a PhD in Statistics in the United States and am applying to postdocs. My undergraduate studies were done in a top 5 institution; my grad school is top ~25. I saw that my undergraduate adviser is looking for a postdoc, and it seems like a good fit.

What is the proper protocol to apply for a position with a professor with whom you already have a working relationship? Would it be appropriate to send them an email to indicate my interest in the position (along with say a cover letter and CV)? Wording this email has been a little difficult, as I'm trying to avoid sounding like I'm leveraging my connections with them to get this position. Is applying to a postdoc sponsored by a former adviser something that one should avoid doing? What else should one take into account in such situations?

For more context, I have been keeping up with this professor, but not extremely closely (we send each other a few emails a year just to catch up). This person supervised my undergraduate honors thesis and supported my application to graduate school.