He attended lectures in botany under Professor Willem Suringar, also exploring local nurseries and joining the university rowing club.

On his father's death in June 1879, Moore sought to be appointed to the vacant post at the Royal Botanic Gardens at Glasnevin.

He was supported in his bid by a number of Dublin newspapers, and took up the post of curator on 9 September 1879, retaining this office for forty-three years; this title changed to keeper in 1890.

During his tenure he saw to the erection of glasshouses to accommodate the expanding collections of tropical orchids, insectivorous plants, ferns, palms, and cycads.

Unlike his father Frederick's interests didn't lie in the study of Ireland's native flora, but rather in practical horticulture.

He was content to leave the identification and description of new plants to the botanists of the Royal Botanic Gardens, Kew, and the British Museum (Natural History), London.

He also received a knighthood for services to horticulture, from George V on 11 July 1911, and an honorary doctorate of science from the University of Dublin in June 1939.

Moore was most active with the Royal Horticultural Society of Ireland, serving as chairman of its council (1904–6), honorary secretary (1906–45), and president (1945–8), and was awarded its gold medal of honour in 1939.