Is there any application of power law to predict large returns?

Power law basically states that after a certain threshold, probability distribution $p(x)\sim c\,x^{a}$ where $x > x_{min}$, which is often the case for financial time series.

It is also generally advised that estimation of parameter a is difficult as data in the tail is sparse. Can someone refer me to any application of power law in a trading context? E.g prediction of large returns, trading strategies, etc.

You may have a look at what is called: econophysics. Basically, it applies techniques in statistical physics into financial time series, including power law as you mentioned. You may start with:

I'm not expert in this field but hope it help.