WordPress hosted in two places can't upload theme

I recently gained a client who wanted me to design their new theme and host the site. I transferred the .ie to my hosting, installed WordPress (it was already installed by the other webdesign company). Despite freshly installing WordPress on my host it will only let me log in with the log in details from the other company. I saved the content and had intended on designing a new theme so I don’t need the other site. Do they have to remove it at their end for it to work properly? If I try to install a new theme then I get this: “Warning: file_exists(): open_basedir restriction in effect.”

Do you think I have issues with how I’m hosting it or do I have to get the other company to take their installation down?