The designer won the Queen Elizabeth II Award for British Design, at an event hosted by the British Fashion Council.
Mr Nash is both a designer and a choreographer - and was praised for his innovation in styling and his use of new materials.
The event at the Design Museum in London recognised the cultural and trade value of fashion and design.
The award was set up in 2018 to encourage and promote British fashion designers, with the duchess meeting young designers who were being supported by initiatives to help them in the early stages of their careers.
Mr Nash's background in dance and movement was seen as bringing a different approach to design, including for sportswear.
His clothes label was launched in 2018, and reflects influences from his background growing up in a Guyanese family in London
Caroline Rush, chief executive of the British Fashion Council, praised his "unique way of combining function, tech and tailoring".
"His work explores the relationship between performance and menswear and is often showcased through beautiful and show-stopping choreography," she told the awards ceremony on Wednesday.