if I buy a new watch can I continue to use my old watch?

I believe so!

I went from a Series 3 to the Series 8 and both were paired to my phone until I removed the Series 3 and gave it to a friend.

I would have let my daughter have it, but it was one series too old for family sharing.

One iPhone can pair to several watches.

Each Watch can only be paired to one iphone.