Ms Collinge added: “As you can imagine, replacing part of the roof of a historic and large building such as ours is not only a huge and complex task, but it is also expensive.”
The work will focus on the flat roof over the largest gallery space in the 260-year-old building.
Work to the building is scheduled to be carried out in 2025, with the gallery’s exhibition and events programme planned around it.
A new rubberised roof will replace the existing covering, and will also house 60 new solar panels.
Ms Collinge said replacing the roof of the gallery would ensure that it could deliver “diverse, fascinating exhibitions to this beautiful location in the heart of the country, but also substantially reduce our energy use.”