Trebilcock was born in Chicago. He majored in chemistry at the University of Illinois from 1920 to 1922, then from 1923 to 1925, studied painting under Leopold Seyffert at the Art Institute of Chicago. In 1925, he submitted his self portrait to the 28th Annual Exhibition of American Paintings and Sculpture at the Art Institute, and won the Martin B. Cahn prize. He also studied and worked in Paris, Madrid, Florence, and London.
His subjects included prominent business, science, and church figures. Among those who sat for him were President Franklin D. Roosevelt; Benjamin F. Fairless, president of United States Steel; and Oscar of the Waldorf, a well-known manager of the Waldorf-Astoria. His work is in many museums, including the Atlanta Museum of Fine Arts.
Trebilcock received numerous awards and honors for his portrait paintings, including the first Hallgarten Prize from the National Academy of Design in 1931; the Frank G. Logan medal from The Art Institute of Chicago in 1928; and the William M. R. French gold medal from the Art Institute in 1929.
Trebilcock was elected an associate member of the National Academy of Design in 1932. He also belonged to the New York Society of Painters, the Century Association, the Tavern, and Cliff Dwellers Clubs in Chicago and the Chelsea Arts Club in London. For a period of time he maintained studios in both New York and Chicago.