Clark became recognised internationally when he appeared at the Bayreuth Festival, first in 1981 as David, which became a signature role. He performed there in 1984 as the Steuermann in Der fliegende Holländer, in 1987 as Melot in Tristan und Isolde, and from 1988 as Loge and Mime in Der Ring des Nibelungen, two other highlights of his repertoire. He performed them in the production directed by Harry Kupfer and conducted by Daniel Barenboim, and again from 2002 in the production by Jürgen Flimm and Ádám Fischer. Clark appeared at the festival in 16 seasons^[5] and more than 120 performances.^[9]

Clark sang at the Metropolitan Opera in New York City first in 1985, as Stewa in Janáceks Jenůfa. Other roles there included Herod in Salome by Richard Strauss, the Captain in Alban Berg's Wozzeck in 1990, Captain Vere in Britten's Billy Budd in 1992, and Albert Gregor in Janáceks The Makropulos Affair in 1996.^[5][10] He participated there in the world premiere of Corigliano's The Ghosts of Versailles in 1991, described as "the slithery, acrobatic villain" Bégearss, alongside Teresa Stratas as Marie Antoinette.^[11] He appeared at the house in 112 performances over 15 seasons.^[10] In 1991 he took part in the world premiere of Berio's Un re in ascolto at the Opéra Bastille in Paris.^[5]

Clark performed at the Royal Opera House first as Mime in 1995, followed by Captain Verve and several minor roles up to 2018.^[3] He performed the four grotesques in The Tales of Hoffmann in 2008, in John Schlesinger's 1980 production.^[8] He appeared there as the Marne Seargent in the world premiere of Iain Bell's In Parenthesis, a 2016 coproduction with the Welsh National Opera.^[12] He performed at Oper Frankfurt as the Fool in Reimann's Lear and as Hauk-Šendorf in The Makropoulos Case, and returned in the 2010s as Monsieur Taupe in Capriccio by Richard Strauss.^[12] His last role was in the world premiere of Pascal Dusapin's Macbeth Underworld at La Monnaie in Brussels in September 2019