Here is a question and answer posted on Facebook today.
Marius Preibys: Wait, what? Its over now??? What do i do with the client now?
The Elder Scrolls Online: We recommend keeping the beta client installed, so that you're prepared for the next event
So it looks like there maybe another beta test before release. Keep your client installed, you wont need another beta Key as everyone from past beta's are automatically allowed access to the next beta.
Marius Preibys: Wait, what? Its over now??? What do i do with the client now?
The Elder Scrolls Online: We recommend keeping the beta client installed, so that you're prepared for the next event
So it looks like there maybe another beta test before release. Keep your client installed, you wont need another beta Key as everyone from past beta's are automatically allowed access to the next beta.