The plan issued an RFP in January due to the contract expirations of its incumbents, which all submitted bids in the search.
Tacora Capital Management has raised $685 million for its second fund.
The plan was slated to hire replacements for two incumbent core real estate managers last week.
The retirement system will add three active core fixed-income managers to its portfolio.
The city previously issued an RFP for the services in June before quickly canceling the procurement.
The retirement system approved three alternatives commitments at its meeting last week.
The retirement system voted to commit to an additional core real estate manager to diversify its allocation.
The search is due to the contract expiration of its incumbent consultant.
An RFP was issued in May and the district plans to invest $20 million and $200 million under the guidance of the selected firm.