"To inspire the design" means to give ideas, motivate, or influence the creation of a design. It suggests providing a source of inspiration or sparking creative thinking that guides the development of the design. Full definition
The show car has already inspired the design of the new A8, but its coupe configuration might make it into production with very few changes. (topspeed.com)
This is a cozy hotel featuring a resort inspired design with rustic touches. (yampu.com)
The entire collection was a pop of bright colors from various comic - inspired designs for both the men's and women's collections. (samanthamariko.com)