Answer
The beat frequency decreases.
Work Step by Step
We know that the thereminist increases the capacitance by moving his fingers because the resonance frequency is inversely proportional to capacitance. As a result, the resonating frequency decreases. The resonating frequency of the circuit is given as $f_{\circ}=\frac{1}{2\pi \sqrt{LC}}$ and thus the beat frequency -- which is given as $\Delta f=f_{\circ}-f$ -- also decreases.
