Davidson will manage existing partnerships with major brands, such as Sainsbury's Bank, with which it provides car insurance. She will also seek agreements with other brands.
Davidson has headed marketing at esure since the company was founded in 2001. Her replacement is Chris Bowden, who has been promoted from customer marketing manager - a role in which he oversaw esure's direct marketing activity.
As head of marketing, Bowden will take responsibility for developing the esure brand and overseeing its direct and new media campaigns. He will also run the in-house creative team.
Esure is a joint venture between HBOS and Peter Wood, the businessman who shook up the insurance market with the creation of Direct Line.
The company claims that sales have trebled and brand awareness has risen 60% since it signed up Michael Winner as the face of its advertising.
Last month Wood and HBOS launched a sister brand to esure called First Alternative. This provides insurance for high-risk drivers and will also be backed by TV advertising starring Winner.
The film director was hired to write, direct and star in esure's advertising because of his acquaintance with Wood. The collaboration saw the insurer part company with its then ad agency, Delaney Lund Knox Warren.
Since then, esure's marketing activity, including a website targeting Winner-haters, has largely been handled in-house.