There were no objections to the plans and they have now been approved.
The new takeaway is expected to open from 11.30am-10.30pm each day.
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In a report, the planning officer said the new premises was not expected to "present disturbance".
The report states: "The proposed development is not uncharacteristic of the local area with neighbouring addresses comprising similar uses and hours of operation to those proposed with existing flues are located on the roof of the neighbouring units."
A front counter area will have seating space for up to eight people and a kitchen.
Upstairs will house a staff kitchen and toilet facilities, the planning application said.
Campaigners have urged Leeds City Council to “stand up for a place to sit down”, in a row over the removal of seating at the shopping centre.
Residents in Bramley were left furious after 22 benches at the local shopping centre were suddenly stripped away in June by its new owners, LCP.
LCP said the move was made in the best interests of shoppers and that the benches had been an “obstruction”.
But more than 1,000 people have signed a petition calling for all the seats to be restored, as covered in the YEP.Support the YEP and become a subscriber today. Enjoy unlimited access to local news and the latest on Leeds United, With a digital subscription, you see fewer ads, enjoy faster load times, and get access to exclusive newsletters and content. Click here to subscribe.