Just updated MacAir 13 to majave 10.14.6 (18G4032. External HP monitor reports HDMI Inactive, no signal. Monitor works on other devices

Here's a few possible simple solves...

First the reason why, so it makes sense.

When performing updates the computer usually restarts rather than shutting down fully. I've noticed peripherals like scanners and RAID arrays don't always mount on those restarts. It takes a full shutdown and reboot for these connected devices to mount properly.

Shut down your Mac.

Unplug the monitor from your Air.

Turn off the power on the monitor.

Start your Mac normally with the power supply connected.

Plug in the monitor normally.

Plug in the monitor.

If this doesn't work, try a PRAM or SMC reset when you're staring back up.

Steps for these vary slightly by the year and model of your Mac, but generally simple.

https://support.apple.com/en-us/HT201295

Depending of the year of your MacBook Air, It's also possible that the port you're plugging into makes a difference. On some newer machines, the ports on the left side provide / accept more power, which your adapter may require to function. If you're plugged in on the right, try the left.

Finally, check the adapter you're using. Things poop out. The little stuff generally goes first. Crazy, but it happens.

My guess is that with the exception of the wrong port, you'll find that once your monitor is detected, it'll be recognized normally again. Hope this helps.

Fantastic! Happy that worked for you.

Did you update an existing Mojave system or did you upgrade from an earlier version of macOS?

A Troubleshooting Procedure that may Fix Problems with macOS El Capitan or Later

You should try each, one at a time, then test to see if the problem is fixed before going on to the next.

    Be sure to backup your files before proceeding if possible.

1. Shutdown the computer, wait 30 seconds, restart the computer.
2. Disconnect all third-party peripherals.
3. Resetting your Mac's PRAM and NVRAM
4. Reset the System Management Controller (SMC)
5. Reset your Startup Disk and Sound preferences, if needed, after resetting the PRAM.
6. Test in safe mode to see if the problem persists, then restart normally.  Use safe mode to isolate issues with your Mac and Playing Safe - what does Safe mode do?
7. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volume entry from the side list.  Click on the First Aid button in the toolbar. Wait for the Done button to appear. Quit Disk Utility and return to the Utility Menu. Restart the computer from the Apple Menu.
8. Repair permissions on the Home folder: Resolve issues caused by changing the permissions of items in your home folder.
9. Create a New User Account Open Users & Groups preferences. Click on the lock icon and enter your Admin password when prompted. On the left under Current User click on the Add [+] button under Login Options. Setup a new Admin user account. Upon completion log out of your current account then log into the new account. If your problems cease, then consider switching to the new account and transferring your files to it - Transferring files from one User Account to another.
10. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Install OS X then click on the Continue button.
11. Erase and Install OS X Restart the computer. Immediately after the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:

     1. Select Disk Utility from the Utility Menu and click on the Continue button.

     2. When Disk Utility loads select the drive (out-dented entry) from the Device list.

     3. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.

     4. Set the Format type to APFS (for SSDs only) or Mac OS Extended (Journaled.)

     5. Click on the Apply button, then wait for the Done button to activate and click on it.

     6. Quit Disk Utility and return to the Utility Menu.

     7. Select Install OS X and click on the Continue button.