Owners of the shopping centre - Sheet Anchor Investments 2 Ltd - wants to change the former 'The Loft' beauty salon into a tattoo parlour.
The beauty salon at number 36 was closed in October 2021.
In the application form, the owners said they are "looking at ongoing investment in the centre in order to improve occupancy level".
There are 36 units - of which 2 are currently vacant at the centre - the owners said.
There would be no changes to the building’s external appearance within the plans.
"Given that the site is located within Bramley Town Centre, the proposed development is not uncharacteristic of the local area", the application states.
"As such the development proposed is not considered to present disturbance at unreasonable hours. Tattoo parlours are not uncommon within town centres.
"Given the above, it is not considered that the introduction of a new tattoo parlour will cause any detriment to the amenity of surrounding adjacent residential neighbours."
Comments about the plans - available to view here - can be made until May 17.
A target date of May 30 has been set for a decision by the planning committee.