When an HP printer is connected but shows as offline, common fixes include checking and securing the network connection, setting the printer status to online, restarting the printer and router, updating or reinstalling printer drivers, and clearing the print queue or restarting the print spooler service on your computer[1][4].

Key steps you can try:

1. **Check connectivity**: Ensure both the printer and computer are on the same Wi-Fi network or the cable connection is secure[1][4].

2. **Set printer online**: On your computer, go to Devices and Printers, right-click the HP printer, and uncheck “Use Printer Offline” to make sure it’s set to online[1].

3. **Restart devices**: Power off the printer and router, wait 30 seconds, then turn them back on[1][2][3].

4. **Update drivers**: Download and install the latest HP printer drivers from HP’s website or use HP Print and Scan Doctor to diagnose and fix issues[1][2].

5. **Assign static IP**: Assign a manual/static IP address to the printer via its Embedded Web Server (EWS) settings to prevent IP conflicts that cause offline status[3].

6. **Clear print queue and restart spooler**: Cancel all print jobs in the print queue and restart the print spooler service on Windows to clear any stuck jobs blocking printing[1][4].

If these steps don’t resolve the problem, remove the printer from your computer’s devices and reinstall it to ensure proper configuration[4].

These troubleshooting methods are recommended by HP support resources and Microsoft Windows support pages for fixing HP printers that appear offline despite being connected[1][3][4].