The term Manning rule is the informal name for a financial industry rule in the United States: Financial Industry Regulatory Authority (FINRA) regulation, Rule 5320. It prohibits a FINRA member firm from placing the firm's interest before/above the financial interests of a client. For example, when a securities firm is holding a customer limit order (an instruction to buy or sell securities at a certain price), the firm cannot ignore that order and cannot trade for their account using a price that would satisfy the customer's limit order without executing the customer limit order.
The rule is applicable both in normal trading hours and in the extended hours trading sessions.