Possible Public Pension Conflict of Interest – When a Board Member Works for a Fund’s Money Manager

I’m looking for sources who can help me understand conflict of interest standards for public pension plans in the U.S. I am looking into large pension employee retirement fund that has a bank executive on its board, which seems like a conflict of interest, given that the bank also works for the pension plan. It’s the bank that cuts retiree checks, and it also handles a large (several-hundred million dollars) investment strategy for the fund. That seems like a red flag for me, but I’m not very familiar with conflict of interest norms around pension boards – maybe this situation is relatively common or benign. I’m looking for opinions about whether this scenario is problematic, and if it is, what sort of ethical controls a pension board could use to mitigate risk of self-dealing.