Watching a DVD of the 1960s TV series THE INVADERS I heard a music score recycled from the older series, THE OUTER LIMITS.
In early TV "canned" music was pretty standard. The theme might be original but much of the incidental music, or background score, was purchased from a music library.
This started to change in the 1960s (to a degree) when production values ticked up a little.
But if a composer worked on a number of series, certain themes or melodies would be lifted from his other works. Jazz musician Oliver Nelson worked on the Raymond Burr series IRONSIDE for a number of its seasons, and I recall hearing familiar melodies he'd used in that series on some later TV shows where he wrote the score.
Of the the most amusing and somewhat odd experiences was from an Irwin Allen series. I have the DVD set of THE LAND OF THE GIANTS. One of the eextras was a different edition of the pilot episode, which was re-edited from what was aired and was slightly longer. The music score from the episode was very familiar -- it was lifted directly from Irwin Allen's earlier series, LOST IN SPACE !!!!!