When Chet Huntley retired, the Huntley-Brinkley Report became NBC Nightly News. While there were various changes to the anchor lineup, John Chancellor was the lead anchor for most of the next decade. Sometimes he shared the anchor desk with David Brinkley, who otherwise mostly did commentary under the title David Brinkley’s Journal. Ultimately Nightly News, dominant in the days of Huntley-Brinkley, was not able to overtake Walter Cronkite in the ratings. During much of this time, this theme was used to close the broadcast. It was definitely used as early as 1972, but may have been introduced in 1970, when Nightly News debuted. Ray Ellis is the composer, who also did the theme for Today at the time.
One wonders whether Bob Israel had this theme playing in his head when he composed the first “World News Tonight” theme.