I want to remove photos from my old iphone without them being deleted from my new phone.

I'm not sure exactly what you are trying to accomplish. If you are trying to completely clear an old phone that you no longer plan to use, you can use the following procedure and it will not affect anything on your new phone: What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Or if you just want to delete the photos from the old iPhone, you can turn off iCloud Photos on that one device. After doing that, any photo deletions on that phone will not affect your new phone. See: How to turn off iCloud Photos - Apple Support