If approved, the scheme will see a brand new building constructed next door to the current centre, which was built in 1980.
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New tennis courts and football pitches, as well as a replacement skate park and BMX track, would also be installed to replace the site’s ageing facilities.
A statement attached to the planning application said Fearnville “is in need of redevelopment to ensure the east Leeds area has a high quality leisure and wellbeing provision, which is fit for purpose”.
It added: “The proposal seeks to stimulate the whole site with activity and a new lease of life.”
Under the plans, new children’s and teenage play areas would be built, along with “fitness zones” and a cycle path.
More trees would be planted to enhance the surrounding woodland and a court for playing petanque – a game similar to crown green bowls – could be set up.
Coun Arif Hussain, who represents Gipton and Harehills, said he welcomed the new development.
“It’s an old building and it’s been there a long time,” the Labour councillor said.
“It needs to move with the times and I think it’ll especially be great for the people of Gipton and Harehills, who’ll have it on their doorstep.
Fellow ward councillor Salma Arif added: “It’s really exciting for the whole community in east Leeds.
“The new building really will be state-of-the-art and I don’t think there’ll be anything else quite like it in the rest of the city.
“The old centre’s been part of that community for a long time, but we’re in a different place now and we need a new building.”
Plans to close Fearnville and upgrade sports facilities in east Leeds have been long in the making, with the council first touting the idea in 2008.
In 2018, the council was forced to drop plans to build a new secondary school on Fearnville Fields, which neighbours the leisure centre, after widespread public opposition.