How should one partner deal with the step kids?

Let the parent make the guidelines. Never assume any role.

Never talk bad about their mom and be good and kind no matter what they do or say. My step mother was the best!!!! Loved her!

If it should become a permanent relationship, treat them as you would your natural children

Just be yourself and be kind to them. Kids have a way of sensing someone being fake or pretentious.

Treat them like you are their friend and leave the parenting up to their parents.

Like there your own . Kids need guidance..

Behave like an adult. They should treat you with respect but they don't have to love/like you.

They must respect you as an adult. If they don't. Consider that a reflection of your partner.

Maybe find an activity you can enjoy together. Have fun and get to know them at the same time. Like spend the day checking out boarding schools. lol

Some good answers here.
Most important is to discuss with your other half what they think your role should be.

mmh so you bring them the kids and how do you talk wit hthe new gf?