Of the Kneller school of portrait-painting, he disliked the innovations of Sir Joshua Reynolds.
Ellys was consulted and employed by Sir Robert Walpole in the formation of his collection of pictures, and was sent to Holland to purchase from the Princess of Friesland The Virgin and Angels by Vandyck, which was subsequently held in the Hermitage Gallery.
In October 1736 Ellys succeeded Philip Mercier as the principal painter to Frederick, Prince of Wales, He was a member of the committee of artists appointed in 1755 to frame a plan for constructing a royal academy, but he did not survive to see the result of their efforts, because he died on 14 September 1757.
Many of his portraits were engraved by John Faber the Younger, including: Lavinia Fenton, Duchess of Bolton; James Figg the pugilist; Frederick, Prince of Wales; Henry Medley; George Oldham; Lord Mayor Humphrey Parsons; William Wake, archbishop of Canterbury; Thomas Walker, the actor, as Captain Macheath; Robert Wilks the actor, and George Stanhope, dean of Canterbury.
Among engravings by other artists from Ellys's portraits were Kitty Clive, by John Tinney; Sir Charles Wager, by George White; and Edmund Gibson, bishop of London, by George Vertue.