In that ship in July 1758 he grounded and captured several French ships near Brest. In 1759 Palliser participated in the successful British capture of Quebec City, commanding the seamen who landed and took possession of Lower Town. In 1760 Palliser was sent to the Mediterranean Sea to chase a small French squadron which had slipped out of the port at Toulon. He bottled the French boats up at several ports in Turkey. In 1761 Palliser captured a Danish merchant ship from a small convoy off Sardinia, escorted by the Dano-Norwegian ship of the line HDMS "Grønland", in a shrewd operation, where no shots were fired. It was a precarious operation, as Denmark-Norway was neutral in the war, but Palliser had intelligence information informing him that the Danish ships were in fact shipping goods from the Levant to Marseilles for French merchants, a practice, which ended after the incident.