In 1562 (being already a B. D., probably of Paris University), he was selected to accompany Father Nicolas de Gouda (Floris), S.J., on his mission (June to September, 1562) from Pope Pius IV to Mary, Queen of Scots, then lately returned to Scotland, Hay practically took charge of the mission, and conducted de Gouda amid many dangers to the queen's presence in a small room at Holyrood, while the majority of the court were hearing a Calvinist sermon.
Sent to Innsbruck in 1564, he became confessor to the archduchesses of Austria, and gained such favour that he was with difficulty removed to Paris to become rector of Clermont College.
In 1566, Pope Pius V resolved to send Bishop, afterwards Cardinal, Vincenzo Lauro to Mary as nuncio, and Hay was to accompany him.
Before the envoys could return, the queen's refusal became relatively unimportant in consequence of the murder of Henry Darnley (10 February): a crime carried out with the connivance, if not the full consent, of the party in Mary's council from whose influence Father Hay had wished her to free herself.
In 1585, he was sent back the third time to Scotland with Father James Gordon, but was forced to return after two of three years, so harsh was the climate against Catholics.
He was once more placed in high office, called to Rome, and chosen "assistant" for Germany and France, but his health was undermined by the severity of his missionary life, and he soon died.