Annoyingly, depending how you read it, the Fountain Tavern referred to might be in Hilsea and it might be in Portsmouth.

Quote

Extract of a letter from Portsmouth, Oct. 28.

“On Friday last his Grace reviewed the Duke of Richmond, accompanied by Lord Lenox, reviewed a large party of the Dragoons at Chichester, which have been quartered there sometime.

“On Saturday his Grace reviewed the Young Buffs (now in garrison at Hilsley Barracks) on Hilsey Green: They performed all the evolutions of a new exercise to admiration: His Grace went through the whole with them in person. After the review the Duke gave an entertainment to the officers at the Fountain Tavern in this garrison.

Leeds Intelligencer, Tuesday 06 November, 1764 source