You should be able to install the required dependencies by opening the Terminal (Ctrl+Alt+T) and entering this command:
sudo apt install python-dev libcups2-dev libusb-1.0.0-dev libtool-bin libcupsimage2-dev libcrypto++-dev libssl-dev libsnmp-dev libsane-dev python-qt4 python-qt4-dbus python-pyqt5 python3-pyqt5 python-dbus.mainloop.pyqt5 python3-dbus.mainloop.pyqt5 python-notify xsane libdbus-1-dev
Afterwards, you should be able to follow the official instructions to install the latest version of HPLIP: https://developers.hp.com/hp-linux-imaging-and-printing/install/install/index