Should new kitten be fully vaccinated before introducing to an existing family cat?

We recently adopted a 9 week old kitten. We took her to the vet who confirmed she is dewormed, and that she is due for more shots 4 weeks from the date of her last shots.

We also have a 7 y/o cat who is up to date on shots as of a few weeks ago.

We have the kitten staying in her own spare bathroom for the time being, but we would like to start the slow introduction process as soon as safely possible.

Would we be putting the older cat at any risk if we were to **not wait until getting the kitten the rest of her shots?

Hoping there's something vet professionals here who could offer some advice. Cheers!