In 1695 he became the leading bass singer in the company with which Henry Purcell worked, playing roles such as the magician Ismeron in The Indian Queen, where he sang the major aria "Ye twice ten hundred deities". After Purcell's death he continued to work for composers Daniel Purcell and Jeremiah Clarke. Richard Leveridge also began to compose himself, and in 1698 all three provided music for The Island Princess, in which Leveridge's performance was widely acclaimed.
Two books of his songs were published in 1697 and 1699 and his popular theatre songs also appeared as single sheet music. After a spell in Dublin he returned to London in 1702 for a revival of The Island Princess and a new production of Macbeth billed as "with music Vocal and Instrumental, all new Composed by Mr Leveridge". He sang the role of Hecate in this work for nearly 50 years, and the music remained popular for more than a century after his death.
Richard Leveridge became involved in the new trend for operas in the Italian style from 1705. He then began a short association with Handel in 1713 to 1714‚ and acted in the first performances of Il pastor fido and Teseo and played Argantes in a revival of Rinaldo. Later in his career, in 1731, he played the role of Polypheme in the first public performance of Acis and Galatea, and several of Handel's Italian arias were published with English translations by Leveridge.
In 1714 he moved to work at the new theatre at Lincoln's Inn Fields, managed by entrepreneur John Rich. Remaining there for most of his career, he returned to his English repertoire and a new form, the musical afterpiece. These lightweight works were often comic, and in 1716 Richard Leveridge produced his own afterpiece, Pyramus and Thisbe. For this comic parody of Italian opera, he wrote the music, adapting the words from Shakespeare's "A Midsummer Night's Dream", and sang the role of Pyramus.
From the 1720s he was the leading bass at Lincoln's Inn Fields and then at Covent Garden. His repertory exploited his firm and powerful voice, and his tunes often became popular favourites. He composed over 150 songs, and is best known for the patriotic ballad "The Roast Beef of Old England".
In between engagements Richard Leveridge ran a coffee shop in Tavistock Street near Covent Garden, but enjoyed good health and reduced his performances only in the last few seasons before retiring in 1751.