The plan is searching to replace Liza Crisafi, who will retire in July.
New $4 million commitment was made to a new manager in February.
The consultant will advise the fund and monitor current providers MissionSquare Retirement and Nationwide Retirement Services.
Plan rehired incumbent firm originally hired in 2017.
The plan is set to discuss potential changes to its strategic asset allocation, including decreasing private equity and traditional credit.
City is searching for a firm to help oversee its $115 million portfolio.
The two will assist with deal diligence and execution, the firm said.
The transaction adds new capabilities in European equity, investment grade credit, sustainable impact equity and green bonds.
They will provide risk management, strategic asset allocation and other consulting services.
The plan approved an infrastructure commitment with an existing manager last week.