The son of Major John Arthur Moore and Sophia Stewart Yates,[citation needed] Moore was an India Office official from 1858 to 1887, holding the role of Assistant Secretary, Political Department from 1875 to 1885.

[2] Moore made a first ascent during his first visit to the Alps in 1862 and immediately became a central figure in the golden age of alpinism.

Moore's first ascents include: This last route, the Brenva Spur, was the first to be climbed on the remote southern side of Mont Blanc and exceeded in difficulty anything that had thus far been attempted on the mountain.

Moore's description of the Brenva ascent is, according to Claire Engel, 'amongst the finest Alpine tales in existence'.

[3] Moore went to the Caucasus with Douglas Freshfield, Charles Comyns Tucker and the guide François Devouassoud in 1868, making the first ascent by a non-native of Mount Elbrus (the lower of the two summits), the highest mountain in the Caucasus,[4] and the first ascent of Kazbek with the same party.