It depends on how the relationship is between your partner and his ex. Do they get on ok or is the partner high conflict?
My DHs ex is very high conflict. Some boundaries we have in place that have worked for us are:
The ex is blocked and can't contact me directly.
Communication should be only about the kids and strictly necessary. All other messages are ignored.
DH runs any changes to the schedule past me first and we don't cancel our plans because ex needs childcare on her time.
In terms of the kids, you'll need to discuss your involvement. If he expects you to look after them then he should also allow you to discipline if needed. Discuss what boundaries he has with the kids. Do they have a set bedtime routine, does he discipline them or is he a Disney dad who lets them away with anything.
But really it depends on your situation, how the ex behaves.l and how your partner parents. No one can really tell you what boundaries you'll need without knowing what's been happening. If the ex is pleasant you might not need the same boundaries. The main thing is that you partner listens to you if something is making you uncomfortable and that he takes your feelings into consideration.
If he thinks the kids should always come first no matter what and that he can't prioritise you, then he's not ready for a romantic relationship.
Some people might say you're jumping the gun a bit with this post since it's only early day but there would be far fewer posts on the step-parenting board if people actually thought about these things in advance.