The company was founded by Frank McNab and Angus Maitland who used mostly JAP V-twins prior to WWI, and the machines were regularly seen at Brooklands in the late Edwardian era.
Postwar, they also used British Anzani four strokes and Peco two-strokes. Maitland had left the company in 1911, and McNab spent the war years in the Royal Navy where he rose to the rank of Lieutenant Commander. After the armistice he was joined by Rob Steward (also ex-RN) and his wife Gwenda, of Morgan fame. All three raced motorcycles at venues including Brooklands, and their customers included the Duke of York, soon to become King of England. His bike, a 998cc Trump-Anzani, was raced by SE Wood, the Duke's chauffeur.
"After the war Gwenda looked around for an activity which offered some of the excitement of her wartime career. She found it in motor cycling, and during the harsh European winter of 1921 she set up a 1000-miles record on a Ner-a-Car under official ACU scrutiny. Then, in 1922, she rode a 249cc Trump-JAP at Brooklands to break 'Double-12' records...."
"Not many women have broken records on two, three and four wheels. Gwenda Stewart, also known as Hawkes and Janson, began by racing a motorcycle, then a Morgan three-wheeler, then a series of cars. She attempted her first motorcycle speed record in 1921 at Brooklands. Between 1921 and 1930, she set a whole series of motorcycle speed records, for endurance and top speed, at Brooklands and Montlhéry. Among her chosen machines were those by Ner-A-Car, Trump and Terrot, the latter two being JAP-engined."
A fine example of a Trump-JAP machine is in the collection of the National Motorcycle Museum, UK.
There is no connection with the ill-famed American real-estate mogul whose family name was Drumpf, nor to the similarly named Trumpf, of Germany.
Sources: The Classic Motorcycle magazine, motorsportmagazine.com, et al.