Gilbert was the son of John Garner Arrow of Streatham, London. He initially trained as an architect but took an interest in insects from 1896 during which time he was a Deputy Keeper on the staff of the Natural History Museum in London from 1896 until 1938. He worked mainly on the Coleoptera and noted stridulation in the larvae and adults of Lamellicorn beetles.
Sound-production in the lamellicorn beetles. Transactions of the Entomological Society of London (1904)
On the characters and relationships of the less-known groups of Lamellicorn Coleoptera, with descriptions of new species of Hybosorinae, etc. Transactions of the Entomological Society of London 57: 479-507.(1909)