Landscape architecture is among the talent needed for the team, which will also include architects, engineers and interpretation specialists and landscape designers.
The charity aims to restore the Grade l listed, 18th-century Palladian house, near Guildford after a fire in April 2015 and transform the visitor experience, in a £30m project.
The competition jury will be chaired by Sandy Nairne, National Trust Board of Trustees member, and former director of the National Portrait Gallery.
The trust has developed its vision for the project over the two years since the fire by taking an informed, open and inclusive approach, commissioning detailed research, surveys and studies, and also listening to statutory bodies, amenity societies, neighbours, members, community groups and local stakeholders.
Competition teams should be led by an architect and demonstrate multidisciplinary expertise in design, conservation, structural engineering, mechanical and electrical engineering, interpretation and landscape design. Creative collaborations are encouraged and additional skills may be proposed.
Competitors must fill out the online form on the competition website and upload documents detailing their project understanding, proposed team and relevant experience. No design is sought at the first stage of the competition. The full jury will be announced at the competition’s second stage.
The deadline for expressions of interest is 2pm on 21 April. The five or more teams shortlisted for the second stage of the process will receive further briefing before creating their concept designs.
The shortlist will be announced towards the end of May. In late summer the concept designs will be displayed digitally and in a public exhibition at Clandon with opportunities for public and stakeholder feedback. Subsequently, the competition jury will meet to interview the teams, review the designs and select a winner.
The winning team is expected to be announced in early autumn 2017 and construction work is expected to begin by early 2019.
Clandon Park is architecturally significant for capturing the moment in England when the Baroque was making way for Palladianism. Designed by Venetian-born architect, Giacomo Leoni, its celebrated interiors were concealed within its austere red brick form. Prior to the fire, the glistening white, double-height Marble Hall, with allegorical figures extending from the ceiling, was one of the house’s showpieces.
The gardens at Clandon Park re-opened in September 2015 . They were Lancelot 'Capability' Brown's penultimate design and the designs he created were completed in 1814. Leading 17th century garden designers George London and Henry Wise also worked on the gardens.
Director-general of the National Trust Dame Helen Ghosh said: "The National Trust is delighted to invite the best talent from around the world to enter this design competition for the restoration and reimagining of Clandon Park.
"A masterwork of its time, Clandon now needs a sensitive, thoughtful restoration of some of the principal staterooms on the ground floor as well as new, multi-use galleries and visitor spaces on the upper floors to showcase the Trust’s and other collections, encourage new creative partnerships and draw new audiences.
"Clandon is so historically resonant and has such cultural potential that we want the competition to attract the most talented design teams with the freshest thinking to help us bring it back to life."
Clandon Park’s project director Paul Cook said Clandon Park has exceptional aura and history and a strategic Surrey position surrounded by potential new visitors.