Genting Casino tabled a proposal to use the first and second floors of grade II*-listed Terminus House.
The establishment in Terminus Terrace currently operates gambling facilities on the ground floor of the building, which was previously a railway station dating back to the 19th century.
The plans will see the upper levels of the premises converted from vacant office space into a new gaming area and bar on the first floor, and staff space on the second floor.
Other changes in the proposal include ramp access throughout the ground floor and a unisex wheelchair-accessible toilet.