All the planes you have obtained are available in the progression tree, in the Planes menu, located in the bottom-right corner of the Hangar screen. You can freely swap them between selected hangar spots by choosing a plane from the tree and picking the one to be replaced at the bottom of the screen.
If you don't currently have free hangar space, your new aircraft will be added to the ones you own, but you’ll need to swap it manually with any active plane from the hangar.