The son of an army officer from Enniskillen, County Fermanagh, Gore studied medicine at Trinity College Dublin, graduating in 1897 and practising until 1901.
After a stint abroad, during which he worked as a ship's surgeon on sailings to North America, India and Italy, he returned to London and the Slade, studying there from 1900 until 1904.
Whilst there he befriended Sir William Orpen and Augustus John, sharing a studio with the latter.
In 1905 he first exhibited with the RHA and from then until 1939 he contributed over a hundred works to their annual shows.
Flower painting in particular attracted him, and it was on his encouragement that the Royal Horticultural Society of Ireland first hosted an exhibition of Flower and Garden Paintings at the Metropolitan School of Art in the 1940s.