If you are a non-petclass, you should recall your current pet if it is out, go to the Formation window (Alt+Y) and remove the pet from it. Then drag the new pet towards it and you can summon the new pet. Since petclasses have multiple slots in their formation window, they can simply recall their current pet, click the icon for the new pet, and summon it. Or, if they can dual-summon, they can summon their new pet while their current pet is out.