Crystal structures with degenerate electronic orbitals are unstable towards lattice distortions that lift the degeneracy. Although these Jahn–Teller distortions have profound effects on magnetism, they are typically unaffected by the onset of magnetic ordering because of a separation in energy scales. Here we show the contrary case in Pr₂Zr₂O₇, where orbital degeneracy remains down to the millikelvin range due to an interplay between spins and orbitals. Pr₂Zr₂O₇ is a multipolar spin ice with strongly localized 4f electrons in an even-number configuration, giving rise to a non-Kramers doublet that carries transverse quadrupolar and longitudinal dipolar moments. Our study of ultrapure single crystals of Pr₂Zr₂O₇ finds comprehensive evidence for enhanced spin–orbital quantum dynamics of the non-Kramers doublet. This dynamical Jahn–Teller effect is encapsulated by the liquid–gas metamagnetic transition that is characteristic of spin ice being accompanied by strong lattice softening. This behaviour suggests that a spin–orbital liquid state forms on the pyrochlore lattice at low temperatures and low magnetic fields.