The head of the new host, SkySilk of California, says Parler is "taking the necessary steps to better monitor its content."
U.S. District Judge Barbara Rothstein said the social network had fallen short in demonstrating the need for an injunction forcing it back online.
The Fox News host compared the right-wing app being deplatformed to the Nazis' deadly attacks on thousands of synagogues and Jewish businesses in 1938.
Amazon joined the growing list of companies cracking down on incitement to violence in the wake of the Capitol attack by Trump supporters.
The vicious messages on social media site Parler stunned the town's mayor, who condemned Lang Holland's posts.
The self-proclaimed "unbiased" alternative to Twitter requires users to agree to pay Parler's legal bills if it gets sued over their posts.