Trying to wrangle those Creatures can take up quite a bit of space, so store extra ones you don't need, or aren't working on, in Isle Storage.
To do so, drag the Creature to the Storage icon, or tap the Creature and choose to send to storage.
Need to retrieve a Creature from Storage? Open it up and drag that Creature to an empty space on the Isle.
Note: Running out of room, even in Storage? You can purchase additional storage spaces with Rubies.