The text-books were David Derodon, Franco Burgersdyck, and Eustachius de Saint-Paul; Grove devoted himself to Jean Leclerc, Richard Cumberland, and John Locke.
The Somerset presbyterians met to arrange for carrying on the Taunton Academy, and appointed Grove, in his twenty-third year, tutor in ethics and pneumatology.
He lived at Taunton, and took charge of the neighbouring congregations of Hull Bishop's and West Hatch, with James Strong.
Early in 1725 Stephen James, the divinity tutor, died, and Grove, without relinquishing his other work, took his place, with the assistance of his nephew, Thomas Amory.
He refused to take any share in the doctrinal disputes which spread from Exeter to London in 1719, and produced the rupture at Salters' Hall.
His orthodoxy was called in question by John Ball, especially because of his discourse on saving faith (1736); but though he laid great stress on the reasonableness of Christianity, and on the moral argument for a future state, he avoided speculations on the doctrine of the Trinity.
He was buried at Taunton, where there is a tablet to his memory in Paul's Meeting, bearing a Latin inscription from the pen of John Ward of Gresham College.
His last Spectator was included by Bishop Edmund Gibson in his edition (1731) of Joseph Addison's Evidences of the Christian Religion.
The lists of subscribers to his posthumous works include the names of Archbishop Thomas Herring, with Hoadly, Secker, and Hutton among the bishops.