Absolute best thing is to bring them to the local shop and ask the pro at the desk.
I made sure to have skis with me when I bought new boots...but the best way is to start with the boot, then find a bindin
Thanks for reaching out!
The answer to this question is going to depend on a few factors, the most important of which is what kind of bindings you have. Generally speaking, most downhill ski boots will be compatible with downhill ski bindings, unless one of the pieces is an older style, designed for a specific purpose (i.e. a tech binding designed for alpine touring), or no longer indemnified by the manufacturer of the binding.
As suggested by @Your_mother, your best bet is to take your skis and bindings to your local REI ski shop and have them see if the bindings are indemnified (allowed by the manufacturer to be serviced by a ski shop). If they are, you are good to purchase new ski boots and have your current bindings adjusted to fit your boots (length) and skiing style (DIN setting on the binding). Bindings do come in sizes (typically by length to accommodate larger ski boots), so as long as you aren't trying to fit a significantly larger size of boot into your bindings, it is likely they will be compatible. If they are not indemnified, you will need to purchase new bindings if you want them adjusted by a ski shop to your new boots.
Hopefully this helps, thanks!