We report on terahertz spectroscopy of quantum spin dynamics in α-RuCl_{3}, a system proximate to the Kitaev honeycomb model, as a function of temperature and magnetic field. We follow the evolution of an extended magnetic continuum below the structural phase transition at T_{s2}=62 K. With the onset of a long-range magnetic order at T_{N}=6.5 K, spectral weight is transferred to a well-defined magnetic excitation at ℏω_{1}=2.48 meV, which is accompanied by a higher-energy band at ℏω_{2}=6.48 meV. Both excitations soften in a magnetic field, signaling a quantum phase transition close to B_{c}=7 T, where a broad continuum dominates the dynamical response. Above B_{c}, the long-range order is suppressed, and on top of the continuum, emergent magnetic excitations evolve. These excitations follow clear selection rules and exhibit distinct field dependencies, characterizing the dynamical properties of a possibly field-induced quantum spin liquid.