My partner wants to have unprotected sex with a new partner, and I'm not comfortable with that

I’ve been dating a man for a year and he’s shown interest in an old flame of his. He wants to have unprotected sex with her. How do I tell him I feel uncomfortable with him having unprotected sex with this person (despite the both of them being tested and coming back clean)? The relationship feels too new to add another person (of that year of us dating was me waiting for his NRE with his other partner to die down) much less have unprotected sex with someone. Any advice?

There are two completely different issues in your question: 1.) that you don't want him having unprotected sex with other people and 2.) that you feel that your relationship isn't in a place where him starting up a new relationship will be healthy.

They're two different issues, but they actually have the same solution - talk to him! Tell him exactly what you told me: that safe sex is an absolute non-negotiable for you in this arrangement, and that you would not be comfortable dating him if he has unprotected sex with other people. This one shouldn't really be a conversation, it's you informing him of your boundary and what you'll need to do to keep yourself safe if that boundary is crossed. If this is non-negotiable for you, don't negotiate about it. 

Then, probably in another conversation, let him know that you had a hard time waiting out his NRE with another partner and worry about the impact on your relationship if he starts up a new relationship. Give specific examples of the way his NRE-influenced behavior impacted you and what you're concerned about this time around. This one should have more back-and-forth where you two both express where you're coming from and hopefully find a way forward that lets him pursue the relationships he's interested in while making sure your needs are met.