Li7 nuclear magnetic resonance and terahertz (THz) spectroscopies are used to probe magnetic excitations and their field dependence in the hyperhoneycomb Kitaev magnet $\beta$-Li2IrO3. Spin-lattice relaxation rate (1/T1) measured down to 100 mK indicates the gapless nature of the excitations at low fields (below Hc≃2.8 T), in contrast to the gapped magnon excitations found in the honeycomb Kitaev magnet $\alpha$-RuCl3 at zero applied magnetic field. At higher temperatures in $\beta$-Li2IrO3, 1/T1 passes through a broad maximum without any clear anomaly at the Ne{\'{e}}l temperature TN≃38 K, suggesting the abundance of low-energy excitations that are indeed observed as two peaks in the THz spectra; both correspond to zone-center magnon excitations. At higher fields (above Hc), an excitation gap opens and a redistribution of the THz spectral weight is observed without any indication of an excitation continuum, in contrast to $\alpha$-RuCl3 where an excitation continuum was reported.