Moore was a member of the Metropolitan Opera Orchestra (1942-1985, principal 1942-1964), and also held positions in the National, Pittsburgh and NBC symphony orchestras.

Among his teachers were Lorenzo Sansone, Josef Franzl and Anton Horner.

An article in the April 1986 issue of The Horn Call states, "Whether lasting through a Salome, pounding out a Long Call, backing up NBC script shows, or playing in Xavier Cugat's orchestra, Dick served his Art well ... Loyal to his colleagues and dedicated to his students, Dick Moore demanded much of himself in maintaining the highest standards of teaching and performance."