Hi @kateaird.Welcome to Apple Support Communities, and congratulation on your new Apple TV.
Unfortunately the latest generations of Apple TV only output video through an HDMI port. While the first generation also had component video and RCA stereo audio ports, they were removed in the second generation.
However, there are HDMI to 3RCA 3-RCA Video Component converter which you can purchase, to connect your Apple TV to a TV that does not have HDMI port.
I hope that helps.