Incumbent agency Hills Balfour declined to comment.
Frank has been tasked with promoting Israel as "the ultimate holiday destination" by raising awareness of Tel Aviv and Jerusalem among UK travellers in what is believed to be a three-year, six-figure budget brief.
According to the agency, it will achieve this by "bringing to life" IGTO's Two Cities One Break brand slogan and through its work supporting the tourist board at travel industry event World Travel Market in November.
The brief includes consumer and trade PR, as well as press office duties, social media handling and media relations.
Frank co-founder Graham Goodkind said: "I love Israel and am lucky to have been there on numerous occasions. We are really looking forward to bringing to life the Two Cities One Break platform to encourage even more Brits to travel to Israel."