Which of the following conditions does not require a procedure turn or HILPT?

Flying a published "No PT" course is the condition that does not require a procedure turn or holding in lieu of procedure turn (HILPT). When a chart specifies "No PT," it indicates that aircraft are not required to execute a procedure turn for that particular segment of the flight. This designation simplifies the approach by allowing pilots to continue their route directly to the final approach fix or waypoint, making the approach more efficient.

In contrast, when a pilot is cleared for a "straight-in" approach, they are typically not required to perform a procedure turn, but they must be aligned and configured to approach the runway directly; this can still involve some procedural limitations depending on the airspace or operational considerations. Establishing in holding on the procedure turn course generally indicates a situation where a procedure turn would be necessary if the approach dictates such a maneuver, often found in traditional instrument approaches. Finally, conducting a "timed" approach can also imply specific requirements for turns or holds depending on the type of operation and the air traffic control instructions but does include procedure turns under certain conditions.

This understanding of the rules and requirements of procedural turns helps enhance the safety and efficiency of flight operations, providing critical context for pilots navigating instrument approaches.