Old charger on new iphone 13

Yes. Apple encourages it. See the following from Buy iPhone 13 Pro and iPhone 13 Pro Max - Apple

As part of our efforts to reach our environmental goals, iPhone 13 Pro and iPhone 13 Pro Max do not include a power adapter or EarPods. Included in the box is a USB‑C to Lightning Cable that supports fast charging and is compatible with USB‑C power adapters and computer ports.

We encourage you to re‑use your current power adapters and headphones that are compatible with these iPhone models. But if you need any new Apple power adapters or headphones, they are available for purchase.