Considering the use of 'Shortcuts' app in iOS, is there a way to quickly get a shortcut to turn location services ON and OFF rather than poking through the menus in settings?
What Louis said is the simplest way to do it, but if for some reason you require turning it on as part of a shortcut, the closest you are going to get with the Shortcuts app is by enabling voice control and having your device say “Open Siri”. Unfortunately in this case, Apple has made the Shortcuts app to where it will stop running when Siri is activated, and continue after Siri is closed.
You also could have your device say “open settings” and have it tap privacy (assuming the privacy tab is visible when the shortcut runs) and manually navigate to the setting yourself, but that pretty much defeats the main purpose of having a Shortcut. Either way, some type of action is required by the user to toggle Location Services.
If you really really want to automate this, there is one workaround, although it takes a bit more effort than it may be worth. You need to have 2 iOS devices; the first device needs to have Voice Control enabled. The second device will need to be close to the first device with the audio at about 50% at least. The second will run the shortcut that plays audio to the other device to tell it what to do. It will say: “Open settings”, “Swipe up Airplane Mode” (in case you are in landscape view), “Tap Privacy”, “Tap Location Services”, “Tap Location Services”, “Tap Turn Off” (in case you are turning it off, it will tell the prompt to disable the setting).
This is a link to the shortcut: https://www.icloud.com/shortcuts/86929b1cd7074d7e81898284135ee4ad
Again, a bit of an odd way to do it, but there aren’t many other ways. Also note that this only works some of the time; annoyingly, sometimes Voice Control doesn’t understand what it is being told to do. But it should hopefully work most of the time.
Building upon user 6209's answer that recommends using Siri to turn off location services, here is my answer as per iOS 12.
Keep doing it as long as Siri doesn't add a shortcut itself in iOS spotlight suggestions(drag down on home screen). When it does, go to Shortcuts app and assign that suggestion to a shortcut. You might also want to put it on your home page as an app, in case you cannot speak at the moment.