Conditional Clearances: "After the Landing Traffic..."
Sometimes the runway is not immediately clear, but the tower anticipates it will be within seconds. To save time and reduce radio traffic, the controller may give you a conditional clearance. This means: "You are cleared for takeoff, but only after this specific condition is met."
The most common conditional clearance is based on traffic:
"Cleared for takeoff after the landing [aircraft type], Runway [number]."
This means you will take off after that aircraft has landed and cleared the runway. You accept the conditional clearance and read it back in full. You remain lined up on the runway, ready to apply takeoff power the instant that condition is met (the landing aircraft crosses the runway threshold and is clearly committed to landing).
Other conditional clearances might be based on:
Departure of other traffic: "Cleared for takeoff after the departing Boeing 737"
Crossing of other traffic: "Cleared for takeoff after the crossing traffic"
Clearance of the runway: "Cleared for takeoff when the runway is clear"
Important safety rule: Do not take off until the condition has been met and you are 100% certain the runway is clear and safe. If you have any doubt, request confirmation from the tower.