"I want to deepen the partnership between our two countries, in particular strengthening our ties in the fields of trade, investment, science, technology and cooperation against shared security threats, and work for progress toward peace."
Mr Quarrey has worked for the Foreign Office for more than 20 years and has served in British missions at the United Nations in New York, in New Delhi and in Harare.
Mr Gould had been in Tel Aviv since 2010 and was the first British Jewish diplomat to be appointed to the role.
