While approaching an ILS course line without a clearance, what is the most appropriate action for the pilot?

Maintaining the last assigned heading and communicating with ATC is the most appropriate action for a pilot when approaching an ILS course line without a clearance. This course of action ensures that the pilot is adhering to the established air traffic control procedures and maintaining situational awareness.

By holding the last assigned heading, the pilot ensures they are not inadvertently conflicting with other traffic or entering an area that they are not cleared to operate in. Meanwhile, communicating with ATC is crucial, as it allows the pilot to seek further instructions or obtain clearance to proceed with the approach. This communication maintains safety by ensuring the pilot is compliant with ATC directives and allows for real-time adjustments based on air traffic conditions.

In this scenario, proceeding to execute an ILS approach without clearance could lead to serious safety concerns, including potential conflicts with other aircraft. Hence, the focus is on ensuring compliance with ATC and avoiding any unauthorized maneuvers.

The other options, such as starting a holding pattern, continuing with the flight plan, or attempting to intercept the localizer, may not appropriately address the need for ATC communication and could lead to violations of airspace regulations.