Don't worry if you do not have the printer disc. You can still install the printer without the printer drive disc. If you have to install Hp printer manually or you have universal serial model, then Windows may automatically detect and install it.
Follow the installation process of a hp printer-
1- Click on the start button on Printers
2- Click Add a printer
3- In the Add Printer wizard, click Add
4- On the Choose a printer port page, then click on Next
5- On the Install the printer driver page, select the manufacturer and model, and then click Next.
If you face any difficulty during or after the Hp printer installation procedure and you are unable to get through it, contact HP support service.