In 1958 Grube obtained a one-year fellowship at the Metropolitan Museum of Art in New York, directed at that time by James J. Rorimer.
Grube held a simultaneous teaching appointment as Adjunct Professor of Islamic Art at Columbia University, In 1968 he was appointed Professor of Islamic and Far Eastern art at Hunter College in the City University of New York.
In 1972 he moved to Italy, first teaching in Padua and Naples, before being appointed as Professor of Islamic art at the University of Venice where he remained from 1977 to 1988.
On his retirement in 1988, he moved to London with his second wife, the art historian Eleanor Sims, an expert on Persian painting.
In London he continued to publish extensively on Islamic art, acting also as editor of a journal he cofounded with Sims.