I wouldn't take the clay out and put topsoil in. The top soil will not make a good base. Anything you put on it will mix in. Here are some ideas;
The consistency of the soil plays a big part in the sub-base at the foundation of your arena. Scientists have identified more than 10,000 different kinds of soil; sandy soils are vulnerable to runoff, while clay-based soils are more stable and harder. Your sub-base should have a slight crown at its center, or be rolled with a 1-to-2- percent grade to allow for runoff.
The base is laid directly on top of the sub-base, just beneath the footing itself. It's often composed of crushed stone, then rolled flat and sealed with chip and seal (the same process used to construct rural roads).
The footing material you choose should be loose, and provide good drainage. If you plan to surround your arena with sod, it's a good idea to line the base and footing area with a pressure-treated board. This keeps the base from shifting under the constant weight of the horses plodding along the rail. Another option is to extend your base and footing beyond your rail or fence. A 20-foot walk track on the outside of your arena provides a cushion for the shifting of the base and footing. The arena's design will impact your footing depth. If you choose the board option, make the footing 2 to 4 inches thick, while an arena with a 20-foot walk track should have footing 3 to 6 inches thick.
Sand deeper than 6 inches can be dangerous for your horses' tendons. Sand breaks down and compacts over time, so start with a 2-inch depth and be prepared to add material regularly over time (ideally in one-half inch increments). Sand also has a tendency to dry out. Products such as Arena RX (available from Midwest Industrial Supply) coat the particles and reduce or eliminate dust.
Rubber does not degrade, and its dark color reduces surface glare on a sunny day. It also absorbs the heat from the sun, keeping the footing thawed on a sunny winter day. Mixing rubber with sand retains these benefits while keeping the footing from becoming too hot. Add 2 pounds of rubber per square foot of sand. The rubber will float in heavy rain; reintegrate it into the sand by dragging the arena with a flat board so as not to damage your carefully prepared base. Buy rubber footing from a horse footing supplier to avoid footing with remaining metal or other foreign materials that may injure your horse.
Although topsoil may seem inexpensive at first, maintaining it is very time consuming. Soil dries out very easily, creating severe dust problems. Soil containing a large percentage of clay is slippery in the rain, and will dry to a very hard surface. In addition, some soils do not drain well, remaining wet for long periods of time. The problem of drainage can be mitigated by adding more than 50 percent sand to the topsoil, but it still needs to be disked daily to maintain a pleasant riding surface.