Frederic Emes Clay (3 August 1838 – 24 November 1889) was an English composer known principally for his music written for the stage. Clay, a great friend of Arthur Sullivan's, wrote four comic operas with W. S. Gilbert and introduced the two men.

While working as a civil servant in the Treasury department, Clay began composing seriously in the early 1860s. His first big success was Ages Ago (1869), a short comic opera with a libretto by W. S. Gilbert, for the small Gallery of Illustration. Other pieces with Gilbert and others followed, and Clay turned to composing full-time after his father died in 1873. That year, he composed a successful opera-bouffe version of The Black Crook for the Alhambra Theatre. Clay's last piece with Gilbert was Princess Toto (1875). He also composed two cantatas. His last two works were both successful operas composed in 1883, The Merry Duchess and The Golden Ring. He then suffered a stroke that paralysed him at age 44.