Clinton was born in Newcastle, the son of a bandsman, and by the age of 17, he had been appointed to Queen Victoria's private band and moved with his family to London. he was a brilliant clarinettist with a clear, solid tone and an immaculate technique. His brother James (1852-97) was also an accomplished player.
George became principal clarinettist in the Philharmonic in 1873 and at the Crystal Palace in 1874. he made many solo appearances and formed the Clinton Wind Quintet in the 1890s. In 1900, he left the royal band and taught at the royal Academy of Music and at Kneller Hall, as well as the Trinity College of Music. George Clinton made improvements to the clarinet, preferring ebonite to wood. He marketed instruments under the name Clinton-Boehm. James Clinton also produced a clarinet, marketed through a company chaired by Sir Arthur Sullivan, but it seems to have met with little success.