The same day Mitch Caplan stepped down as the chief executive of E-Trade Financial Corp. in November, it got a $2.5 billion infusion from a private-equity investor.Nearly a year later, Mr. Caplan is working on such investments from the other side of the table.

Aquiline Capital Partners LLC, a New York private-equity firm that specializes in financial services, said Tuesday that it had hired Mr. Caplan as an executive adviser.

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