Deptford joined from Barings last month and replaces Whittaker with immediate effect.
Whittaker will now focus on the management of the UK growth trust, having produced bottom quartile performance in the IMA UK equity income sector over three and five years.
Deptford was previously head of UK retail equity funds and managed both the Barings equity income and UK growth funds.
New Star Investment Funds managing director Mark Skinner says: ““I am delighted to announce Charles’s appointment. Charles has a proven and consistent track record and I am confident that his considerable expertise will benefit investors in the New Star Equity Income Unit Trust.”