Arrindell was born in Basseterre, Saint Kitts, and educated at the St. Kitts–Nevis Grammar School, where he was top of his class in his final year.

He left to study in England in 1954, and was called to the bar in June 1958, as a member of Lincoln's Inn.

From 1972 to 1978, he served as a senior magistrate, both in Saint Christopher-Nevis-Anguilla (as the colony was then known) and in the British Virgin Islands.

He served in the position until November 1981, when he succeeded Sir Probyn Inniss as Governor of Saint Kitts and Nevis (an Associated State of the United Kingdom at the time).

On independence in September 1983, he was appointed governor-general, and remained in the position until his retirement in December 1995.