1973 was a watershed year for Burrows in which he received the first gold record won by an Australian jazz musician for his record Just the Beginning; instigated the first jazz studies program in the southern hemisphere at the New South Wales Conservatorium of Music and was awarded Member of the Order of the British Empire (MBE). In 1979 he was appointed as chair of the jazz studies department at the conservatorium.
He has performed to normally classical music audiences through tours with Musica Viva and Australian Broadcasting Corporation concert series. Burrows fronted the nationally televised show The Don Burrows Collection for six years. He has an extensive recording career in his own right with his groups, and has performed on many more albums with other artists.
In the 1980s he associated closely with the then young James Morrison, helping Morrison to form his style and develop into the world famous musician he later became. For a time the Don Burrows quartet had a regular weekly lunchtime gig at a major Sydney hotel bar, where high flying stock brokers of the 1980s would meet to hear the hottest jazz in town and schmooze clients. It was perhaps in this period that Don's national fame was at it's height - the master Jazz musician and the young rising star of Morrison performing weekly for a rich and powerful audience whilst a hectic schedule of national tours, special events and television appearances took them to the rest of the country.
In the 2000s Don Burrow's public profile has receded somewhat as he performs less than he used to.
In 2005 he toured with a small band including renowned Australian jazz pianist Kevin Hunt , Burrows is using his photographic images with his music, in a show called Stop, Look and Listen.
He has had a lifelong hobby of black and white photography, beginning in his 20s as an active participant in the Sans Souci and Caringbah camera clubs in Sydney. He sees the creativity of music and photography having significant similarities.
Burrows has suffered from arthritis since age 38. In a 2008 interview with Australian Broadcasting Corporation's Andrew Ford, celebrating his 80th birthday, he said "arthritis is not the greatest for playing a musical instrument. But playing a musical instrument is very, very good for arthritis"