Yagi gain reduction when using off frequency (2.3Ghz WiMax system using 2.4Ghz WiFi Yagi)
The bandwidth of a Yagi antenna is just one of the parameters that was considered in the design. Therefore, there is no definitive answer, since the performance at 2.3 gHz would vary between different WiFi antennas.

Having said that, there is a high likelihood that most WiFi antennas would work. The reason is that WiFi needs 100 megahertz of bandwidth (2401 MHz to 2495 MHz), and it would be difficult to design an antenna with that wide a bandwidth without also being sensitive at 2300 MHz (WiMax). 

But more importantly, a Yagi can be designed for a very wide range of gains, so it really is just a matter of getting one with more gain than your current WiMax antenna. Keep in mind: The more elements in the Yagi, the higher the gain but also the more directional it is. It may be more difficult to point a higher gain Yagi.