Apparently HP ENVY 7645 doesn't work with Mac OS 10.14 Is there any solution? Or do I have to buy a new printer?

The HP ENVY 7645 e-All-in-One Printer (E4W44A)'s Specifications indicate it is Apple AirPrint-enabled. If it is not already installed that way, remove the printer from Printers & Scanners, and add it again. Refer to If you can't print from your Mac or iOS device.

Download and install the 10.13 High Sierra Driver, it works for most HP printers using Mojave.

HP Envy Driver Download

I did not tell you to download anything. No drivers are required to use AirPrint.