The search follows the termination of its active manager last month.
The retirement fund disclosed commitments totaling roughly $2.1 billion in May.
The new vehicle closes with approximately $810 million in capital commitments.
The fund is looking to add buyout, growth, venture capital and GP-led secondaries strategies to its endowment.
The Southern-based private equity firm has hired a managing director for its lower middle market strategy, which was launched last year.
Firm has closed its most recent fund at $1.35 billion.
The commitments include two new manager relationships.
The city made private equity commitments on behalf of its retirement plan and OPEB trust in June.
The private equity fund acquired two companies prior to its final close.
The plan is seeking firms that offer North American-focused fund-of-funds.