Neon Fox Ltd wants the alcohol licence to transform the Bargain Booze shop at 117 Falsgrave Road.
In its application, the company's Director Daniel Wilson said they are planning to convert the off-licence into a restaurant serving freshly made pizzas and craft beer.
The application added that the restaurant intends to have 50 covers and serve different craft ales on draught with a selection of real ales and will be "ideal for families".
It also stated that the restaurant would offer takeaway food and drink by walk-in and delivery.
The new bar and restaurant, which would be called Neon Fox, would be open seven days a week from 4pm until midnight, Monday to Thursday, and 12pm until midnight Friday to Sunday.
The time allowed for alcohol sales would be from the opening hour until 30 minutes before closing, the application adds, and on several days a year, including bank holidays, Boxing Day and New Year's Eve, the bar would be open until 1am.
As part of its application, the restaurant has agreed with North Yorkshire Police's licensing team that the venue will operate mainly as a food-led establishment with a minimum of 30 covers.
Several objections to the plans were also raised, with concerns over crime, noise and public nuisance.
Scarborough Council's licensing sub-committee was set to decide on the application on Tuesday April 12, but a decision could not be reached due to an error during the licensing process and the plans have now stalled.
Councillors said application notice at the premises could not be viewed at times when the shutters were down, and so the legal requirements had not been met.
By law, application notices must be prominently displayed for 28 days where they can be conveniently read by passers-by. It is not clear if or when the applicant will reapply.
Plans to open a "relaxed" wine bar at the vacant William Hill bookmakers on Falsgrave Road were withdrawn in September last year after the owners were refused an alcohol licence.
In June last year, Scarborough Council permitted Belinda Leppington to turn the former Falsgrave Juniors School building on Falsgrave Road into a bar.
The building, known as the Clock Tower and most recently home to the Bed King shop and bed warehouse, is located in one of Scarborough's busiest areas but has been empty for more than three years.