Is it critical to keep your partners updated on new and potential new partners?

if your partner knows you're poly and is 100% ok with you dating other people, do you have to tell them whenever you get another partner (alternatively, do you have to ask BEFORE you get another partner)?

That's totally up to you and your partner to set those terms based on what works for your relationship. In my personal experience, it's wise to keep your partner apprised of what's going on in your dating life - that way nothing feels like a secret (which can feel like cheating) and they aren't caught off guard.

That's not to say that you need to fill out a Notice Of New Partner Form in triplicate and submit it through a Polyamory-Certified Courier every time you date someone new - just that it's probably best, in most cases, to be open with your partners about your dating life! It's up to you and your partners to decide exactly how to do that - do you think it's important to bring it up every time someone goes on a date, or only if you're thinking that things are getting serious with someone? 

I like to share what's going on in my life with my partners! So I let them know "I have a date next week with a guy I'm really into," and then a few weeks go by and the conversation is "I'm really starting to like Kevrick, I think things are going pretty well!" And then by the time I'm referring to Kevrick as "my boyfriend," my other partners aren't like "you have a new what now?"

In my case, however, it's always a case of informing, not asking. I don't say "I really want to start dating Kevrick, what do you think about that?" I don't need my partners' permission to date new people. That's what works for us!

I find it hard to imagine a partnership - in which you share lives and talk about what's going on with you - where you can end up with a new partner and your current partner(s) don't know about it as it happens. In most cases, not informing your partner about your dating life takes extra effort and sometimes even lies of omission.