Previously, the company had its license suspended in London, and current CEO Dara Khosrowshahi has said that Uber is working hard with Transport for London to find the best solution and move things along.
On Monday, Uber begins its appeal against a separate suspension in London, where around 40,000 drivers use the app and serve 3.5 million customers.
The ride-hailing app has already submitted a new application to be able to run minicabs in the city, but the company faces not being able to operate in the city over the Christmas period if it is not processed in time.
Uber and Sheffield City Council representatives did not immediately respond to a request for comment.
The issue in question is that Uber didn't change the name on the licence from former United Kingdom boss Jo Bertram, who announced she was leaving the company back in October.
Survival Game Fade to Silence Announced at The Game Awards (Developing)
You'll be faced with harsh choices on who to recruit and who to leave behind as you build your base. THQ Nordic says Fade to Silence will be a "complex, character-driven, group survival experience".
Uber will be allowed to continue operating until December 18 and, if it chooses to appeal the suspension, it can function until that has been heard.
A Council spokesman explained, "Any new application is dealt with by the Licensing department who will decide if those applying for the licence meet the criteria". "The legislation does not allow for the transfer of an operator's licence".
Uber claims to have informed Sheffield council of the need to change the name on 5th October, only to be told the name couldn't be changed and that it'd have to apply for a brand new licence. The council hasn't suspended the licence for any particular wrongdoing or alleged dodgy practice (which was reportedly partly the case in London).
"We hope our application for a new licence will be resolved before December 19 so that we can continue serving tens of thousands of riders and drivers in Sheffield".