Note: This answer assumes that you are in FAA airspace.
There are two aspects about entering a terminal area to land. First, there is clearance into the terminal area, and secondly, there is clearance to land. Let's look at them separately.
The clearance into the terminal area is dependent on airspace and your flight flan. You do not need a landing clearance to enter the traffic pattern. This is clearance to fly a path in the sky, but is not a clearance to touch anything on the ground. If your terminal area is controlled, you will need to work with ATC to arrange your entry into the traffic pattern. Depending on your entry geometry, this could be a full rectangular left hand pattern as you depicted, they could just give you a long final, or anything in between.
For further reading about FAA classes of airspace, this is a good reference.
Where clearance into the traffic pattern permits a flight path, landing clearance allows the airplane to touch the ground, but does not provide any clearance for path of flight. Thus, if the airfield is controlled, you need to receive a landing clearance before wheels touch the ground. Situationally dependent, you will typically receive landing clearance about when you turn base. It is controller technique to give you an earlier or later landing clearance. You may fly a full traffic pattern expecting to receive clearance, and when on short final it is not received, you have to execute a go around.