The phrase "a website that exists" is correct and usable in written English.
You can use it to refer to a website that is currently active and accessible on the internet.
Example: "I found a website that exists where you can learn about different programming languages."
Alternatives: "an active website" or "a live website".
And let's not forget the website that exists solely to inform the world whether Maldonado has suffered a crash on any given day.
There's nothing to stop 7.7 million fathers from signing up to Dad.info, dadzclub, or one of a number of websites that exist to support dads.
Back in June, we noted a couple of websites that existed for the sole purpose of revving up mayor battles on Foursquare: When Will I Be Mayor? and Be The Mayor.
The Internet Watch Foundation found that 88% of teens' videos and photos are stolen, sometimes by a cottage industry of 'parasite websites' that exist for the sole purpose of harvesting candid teenage photos.
An advocate of celebrating naturally wavy and curly hair, it's been the kickstarter for a slew of blogs and websites that exist solely to tell you how to love and take care of your curls (just ignore the 'girl' bit of the name this is open to anyone on the gender spectrum).
In Britain, Alex Butler, an e-government chief, has closed 551 of the 951 central-government websites that existed in early 2006.
Since there are multitudes of websites that exist as repositories for user-generated content, this concept could be adapted to many other similar applications.
With the growth of the Internet over the years and the number of personal websites that exist on just about any topic, more people are turning to their computers as their first source of information.
There are numerous websites that exist to connect employers with potential employees that are worth exploring.
