According to Historic England, the date of the building coincided with the railway “mania” of the 1840s, making it “an exceptional example of this interesting period in railway history”.
Historic England said it had no objection to the applications on heritage grounds.
Seventy-five parking spaces would be provided as part of the project, along with bike storage and footpath access.
Applicants Ollo Padel said: “The development will seek to support an inclusive, community centred leisure destination, encouraging physical activity, social interaction and wellbeing across all ages and abilities.”
Otley and Yeadon Liberal Democrat member Colin Campbell supported the plans, saying: “It strikes me this is quite a sensible proposal.”
Kirkstall Labour councillor Andy Rontree said: “I’m impressed with this.
“I think it’s an appropriate and imaginative use of the site.”
One of the fastest growing sports in the UK, padel is often described as a cross between tennis and squash and is played on a court around a third of the size of a traditional lawn tennis court.
