No, she's not Jewish despite her head-coverings:
She's Emma Joy Kitchener, the daughter of Hon. Charles Eaton Kitchener and Ursula Hope Luck, born in 1963. She's the great-granddaughter of Henry Elliott Chevallier Kitchener, 2nd Earl Kitchener of Khartoum, and great-grandniece to the more famous Field Marshal Horatio Herbert Kitchener, 1st Earl Kitchener and through him, there is, yes, a connection to the Land of Israel. And even to Jews, in that his death was attributed to a "Jewish conspiracy".
She married Julian Alexander Kitchener-Fellowes, Baron Fellowes of West Stafford and creator and writer of Downton Abbey. She was Lady-in-Waiting to HRH Princess Michael of Kent.
And, most relevant, she's the de facto story editor of Downton Abbey (“She does a whole tier of notes,” said Fellowes, “and I usually do what she says.”).