I sent an email to the Royal Academy of Music the other week, asking about the title of Professor of Music. I received a very helpful reply yesterday advising me that in those days "Professor of Music" was a common term used interchangeably with "Teacher". There was no qualification needed to advertise in this way. So I needn't think my relatives were trying to give themselves a more glorified title. : )
The helpful librarian who wrote back to me then added some extra information unbidden: "[Gustav] Holst’s grandfather [Gustavus Valentin Johann Von Holst, Matthias and Katharina Von Holst's firstborn son] would have been too old to have studied at the Academy: in its early days, it taught only children aged approximately 12-16 years. I checked our records, however, and did find Mathias Von Holst, aged 14, who entered the Academy on the 9th October 1848 and left on the 16th June 1849. He studied piano with Mr Cipriani Potter."
This was Gustavus' first child, also named Gustavus, who was known as Matthias. I found a newspaper article (The Times, 22 Dec 1847) which said a candidate with the name of Von Holst distinguished himself in the examination for two King's Scholarships at the Royal Academy of Music, which became vacant every Christmas. It would appear that he didn't win a scholarship but he went anyway, the following year. Matthias was both a pianist and a harpist.