Gears are a new element in Pokémon Rumble Rush. When you obtain a Pokémon, it will have multiple slots. It will have one slot for a big Summon Gear and one or two slots for a Power Gear. Gears are essentially items that you obtain by refining ore found within the various stages that provide power ups for your Pokémon when attached.
Gears can be upgraded, with each specific Gear having its own upgrade level limit. To upgrade them, you need to get various upgrade elements obtained when you get the Gear. However, you can also send the gears to the Adventure Tour, essentially transferring them, and you'll receive the upgrade elements. Each gear is worth 3 elements.