Unfortunately, there are only specific instances that will reward players with Elite TMs. Sometimes, these items are included in bundles in the item shop, though they'll often cost quite a few PokéCoins — meaning if you haven't been stockpiling your coins, you may have to shell out some real money to get the TMs.

There are also certain events where players will be rewarded with the Elite TM for completing either Special or Field Research tasks, though those are few and far between.

If you're a fan of the GO Battle League, then if you advance far enough through it, you may be rewarded with an Elite TM for winning enough battles — though again, this will require quite a bit of grinding to be successful with.

Unfortunately, beyond this, there is not an easier way to obtain an Elite TM. If you don't already have one, keep your eyes peeled on the shop and for upcoming research events, and be sure to use whatever ones you obtain wisely.