To unlock the new, 'real' Nimbasa City Gym, you must first enter the Old Nimbasa City Gym and defeat the trainers there. The old gym is the one that Elesa used to call home, back in Pokemon Black & White. Now though, she's moved from her amusement park-themed gym to a new, model's runway-themed gym.
The old gym is found west of the Ferris Wheel; the bright building next to the Vending Machines. Inside you'll see loveable Clyde. Feel free to talk to him, then get ready to traverse the gym.
The gym contains a number of rollercoasters. The dashed lines on the coaster tracks signal the path that the carriages will take, so use this to plan ahead. At the beginning, the red track leads nowhere, so jump onto the rollercoaster on the blue track.
Jump off at the next stop. There's a Youngster here, but he's not looking for a battle. Instead, move past him and stand on the blue button to his north. This will change the path that the rollercoaster on the blue track will take. When it stops at your stop, jump back on.
You'll now be taken north. Jump off at the next stop, then follow the path around to the green button. Stand on it to press it. The green path will turn yellow. Now when the next carriage comes along, try and enter it. A Rich Boy will jump you, oh no! Get ready for the battle!
Trainer Battle: Rich Boy
Once defeated, he'll move out of your road. When the next rollercoaster comes, jump onto it. It will take you up and around the gym. When it stops, jump off. Go over and hit the purple switch to turn the purple track orange. When the next carriage comes, attempt to jump on. Oh no! Jumped again! This time, it's a Lady!
Trainer Battle: Lady
Once she's defeated, she'll move out of the road and allow you to jump onto the carriage. Do so. Ride it through the loop to the next stop. Jump off. You're at the end of the gym. Go over and talk to the Beauty. She'll give you a Parlyz Heal and tell you that you can now enter the New Nimbasa City Gym. It's time to leave.
Go over and hit the red switch. The red track will turn pink and the track will be edited to allow the carriage to reach you. When the carriage comes, jump on and ride it back to the beginning of the gym. Leave the gym and head back to the Pokemon Center to heal your Pokemon.
Now it's time to head to Route 5 and get some training in!