Definition
An ATC authorization for a pilot operating under instrument flight rules to conduct any standard or special instrument approach procedure published for that airport. When issued without specifying a particular approach, the pilot may choose which published procedure to fly.
Plain English
Air traffic control has given you permission to fly an instrument approach into the airport, and you can pick which published one to use.
Context Anchor
Heard on IFR radio communications when ATC is authorizing an aircraft to begin an instrument approach toward an airport.
Derivation
Cleared comes from the aviation use of clear, meaning ATC has given permission to do something. Approach comes from older French and Latin roots meaning to come nearer. Together, the phrase means you have been given permission to fly the planned procedure that brings the aircraft nearer to the runway environment.
Why Pilots Care
It provides the legal and safe authorization needed to descend below published altitudes in instrument conditions while maintaining separation from other traffic.
Intuition Check
Cleared Approach does not mean the runway is clear, and it does not automatically mean you may land. It means ATC has authorized you to fly an approved approach procedure.
Example Sentence 1
After checking the weather and winds, the pilot accepted 'cleared approach' and elected to fly the ILS to Runway 27.
Example Sentence 2
After receiving the cleared approach, we configured the flaps and began tracking the localizer.