As a conductor, Alexis Kossenko devotes much of his time to his responsibilities at the head of Les Ambassadeurs ~ La Grande Ecurie; this ensemble is the joint heir to Les Ambassadeurs, of which Alexis Kossenko is the founder, and La Grande Ecurie & La Chambre du Roy, where he took over from the late, legendary Jean-Claude Malgoire.

He is also a sought-after guest conductor: he is in demand by symphony orchestras as well as by phalanges of historical instruments, such as Arion (Montreal), Arte dei Suonatori (Poland), Holland Baroque, European Baroque orchestra, Sinfonia Iuventus (Poland), Academia Montis Regalis (Italy), B'Rock (Belgium), Le Concert d'Astrée (France), {oh!} Orkiestra Historyczna (Poland), the Royal Danish Opera, the Staatstheater Oldenburg (Germany), BaroqueArhus (Denmark), Warsaw Chamber Opera (Poland), JOA (Jeune Orchestre de l'Abbaye), the Lviv Orchestra (Ukraine), the orchestra of the Brunico Academy (Italy), in a repertoire ranging from Lully to Britten, via Bach, Mozart, Rossini, Mendelssohn and Brahms. He is considered an expert in the operas of Jean-Philippe Rameau.

In 2015, he conducted 24 performances of Mozart's Le Nozze di Figaro. He was then invited on several occasions by Sinfonia Iuventus to the Warsaw Philharmonic to conduct Mendelssohn, Reinecke and Brahms (4th Symphony and violin concerto). In 2018-2019, he conducted the Marriage of Figaro at the Royal Opera House in Copenhagen, followed by Les Paladins and Les Boréades by Rameau at the Oldenburg Theatre. At the Atelier Lyrique de Tourcoing he conducted Chabrier's L'Etoile in 2020. With Les Ambassadeurs he conducts Platée, Acante et Céphise and Zoroastre by Rameau (at the Théâtre des Champs-Elysées in Paris), Cosi fan tutte and Mozart's Requiem.

In addition to his duties as Artistic Director of Les Ambassadeurs, Alexis has been appointed Music Director of La Grande Ecurie and La Chambre du Roy from 2020.

Sensing a common future for the two ensembles, he married them in 2021, and it is now at the head of "Les Ambassadeurs ~ La Grande Ecurie" that he is developing his most cherished projects. His new productions and recordings have received rave reviews: The Fairy Queen (Purcell), Le Monde selon Mozart, Zoroastre (Rameau), Carnaval du Parnasse (Mondonville), Mendelssohn symphonies, etc.