The application was submitted to increase the capacity of car park near the new eye clinic by Tarmaccing over a grassed area.
The Mid Yorkshire Hospitals NHS Trust says that despite regulated staff parking permits, there are still issues with workers unable to find spaces within the grounds.
The trust admitted that the workforce tops more than 5,600 with only 1,600 spaces available.
Almost 1,000 new staff members started in the the last year.
In a statement, the trust says further plans for extra spaces are in the pipeline, for both staff and visitors.