Alexander Grove was born in London. His singing career began at the age of seven when he was a chorister and soloist at St Paul's Cathedral in London. He then continued at The Royal Northern College of Music in Manchester and at the Georg Solti Accademia di Bel Canto in Italy.
Grove has participated in several competitions and in 2010 he was named winner in the male singer category of Kiri Te Kanawa's "Kiri Prize" at the BBC in London.
At the Gothenburg Opera, he has performed the role of the Son in Weill’s Die sieben Todsünden, appeared in Ariadne auf Naxos and in Gianni Schicchi.
Alexander has performed over 60 opera and operetta roles such as Don José in Carmen at Malmö Opera (2018) where he has also sung Don Ramiro in La Cenerentola, a role he has also sung at the Finnish National Opera, Magnus Gabriel in Cristina Regina di Svezia, Foroni with Tobias Ringborg at Vadstenaakademien, Gastone in La traviata and Remendado in Carmen at Opera på Skäret, Danilo in Die lustige Witwe at the Scottish Opera, the title roles in Le Nos at Royal Opera Covent Garden, L’amico Fritz at Den Jyske Opera and Erster Geharnischter mann in Die Zauberflöte with Daniel Harding in Lucerne.
In 2017, Grove premiered the role of Dick Gren, specially written for him, in Rickard Söderberg's operetta farce Teaterhotellet at Ystadoperan.