(Thanks to Kanten for the original article.)
Trainer locks are a(n often widely hated) part of many PTCG formats: various Vileplumes over the years, Spiritomb, Seismitoad-EX, Budew, just to name the most egregious offenders. They do exist in RS-PK too, but are fortunately not as widespread, except for one deer that doesn't quite count as a Trainer lock, but has grown to become the unofficial mascot of the format.
If the lock is coming from an attack, you can inflict Special Conditions or other effects that stop attacks to buy turns. Against Manectric ex, Dragonite ex δ, and Crobat δ, walling them with Resistance or damage reduction is effective.
If the lock is coming from a Poké-Body/Power, cards that shut those off will counter them.
By far the most common type of Trainer lock you will encounter. The big targets that these lock out are:
Holon Transceiver
Rare Candy
Windstorm and Stadiums (so you get to keep your own Stadium in play)
Pow! Hand Extension
Cessation Crystal
With the exception of Crobat δ, Cessation Crystal is actually a problem for Trainer lock decks. With Houndoom and Vileplume ex, it's clear why. Manectric ex needs to keep Cessation Crystal off the board so that Mew ex's Versatile works, and Dragonite ex δ needs to do that so Latios ex δ will have 0 Retreat Cost, and the sequence of get Confused → attach Warp Energy → promote Latios ex δ → retreat back to Dragonite for free remains possible.
While Disconnect and Deafen can stop Cessation Crystal from being played, it will not remove already-played ones, or ones that have been snuck in during a turn where the Trainer lock was not maintained. Thus, these decks still run small quantities of Windstorm.
(Vileplume ex needs to be Active for Block Dust to work, so you can play a (non-Trainer!) forced switch card to send it to the Bench, then seize the opportunity to attach Cessation Crystal to your Pokémon. This keeps Block Dust disabled when Vileplume comes back in.)
Manectric's Basic form has a Trainer-locking attack too, and it even covers Supporters.
Limitation locks Supporters, which is devastating early-game.
Night Vision can be used to check if Admin will help or hinder the opponent before playing it.
Frequently abused with Swoop! Teleporter to increase the odds of starting with it.
Primal Lock locks Pokémon Tools (Cessation Crystal being the main culprit), and clears the opponent's side of existing ones.
Chilling Breath locks all types of Trainers for a turn.
Since it's a Stage 2, it's only played in its own dedicated deck.
The "stupid deer" locks Trainers, in a sense, by discarding them from your hand with Push Away. You can't play Trainers if they're in your discard pile, and if you're out of Windstorm or Stadiums, then the Stantler player's Cessation Crystals and Stadiums will stick.
Push Away is a big reason why players use Warp Energy (to switch out Pokémon that have been Confused by Screechy Voice, or Pow-ed in) and Cyclone Energy (to counter the Cessation Crystal attached to Stantler).