Arundell held a number of administrative positions, principally in the West Country. He was the first receiver of the Court of Augmentations for Cornwall, Devon, Somerset and Dorset, and in 1533 succeeded his father as Receiver-General of the Duchy of Cornwall. He was a Justice of the Peace for Cornwall, Dorset and Somerset during the reigns of Henry VIII and Edward VI, and was appointed to commissions for gaol delivery, oyer and terminer, and the defence of the counties of the south-west coastline. He commanded the Dorset militia during both the Pilgrimage of Grace in 1536–7, and King Henry VIII's expedition to France in 1544. He was twice High Sheriff of Dorset and Somerset (1531), was keeper of the royal parks in Dorset, and in 1539 sat on the Council of the West with his father. He was elected Member of Parliament for Dorset in 1545 and 1547.