$^7$Li nuclear magnetic resonance (NMR) and terahertz (THz) spectroscopies are used to probe magnetic excitations and their field dependence in the hyperhoneycomb Kitaev magnet $beta$-Li$_2$IrO$_3$. Spin-lattice relaxation rate ($1/T_1$) measured down to 100,mK indicates gapless nature of the excitations at low fields (below $H_csimeq 2.8$,T), in contrast to the gapped magnon excitations found in the honeycomb Kitaev magnet $alpha$-RuCl$_3$ at zero applied magnetic field. At higher temperatures in $beta$-Li$_2$IrO$_3$, $1/T_1$ passes through a broad maximum without any clear anomaly at the Neel temperature $T_Nsimeq 38$,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 re-distribution of the THz spectral weight is observed without any indication of an excitation continuum, in contrast to $alpha$-RuCl$_3$ where an excitation continuum was reported.
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