Li nuclear magnetic resonance and terahertz (THz) spectroscopies are used to probe magnetic excitations and their field dependence in the hyperhoneycomb Kitaev magnet β-Li 2 IrO 3. Spin-lattice relaxation rate (1/T 1) measured down to 100 mK indicates the gapless nature of the excitations at low fields (below H c 2.8 T), in contrast to the gapped magnon excitations found in the honeycomb Kitaev magnet α-RuCl 3 at zero applied magnetic field. At higher temperatures in β-Li 2 IrO 3 , 1/T 1 passes through a broad maximum without any clear anomaly at the Néel temperature T N 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 H c), an excitation gap opens, and a redistribution of the THz spectral weight is observed without any indication of an excitation continuum, in contrast to α-RuCl 3 where an excitation continuum was reported.