We present an experimental study of the quantum spin ice candidate pyrochlore coumpound przr by means of magnetization measurements, specific heat and neutron scattering up to 12 T and down to 60 mK. When the field is applied along the $[111]$ and $[1bar{1}0]$ directions, ${bf k}=0$ field induced structures settle in. We find that the ordered moment rises slowly, even at very low temperature, in agreement with macroscopic magnetization. Interestingly, for $H parallel [1bar{1}0]$, the ordered moment appears on the so called $alpha$ chains only. The spin excitation spectrum is essentially {it inelastic} and consists in a broad flat mode centered at about 0.4 meV with a magnetic structure factor which resembles the spin ice pattern. For $H parallel [1bar{1}0]$ (at least up to 2.5 T), we find that a well defined mode forms from this broad response, whose energy increases with $H$, in the same way as the temperature of the specific heat anomaly. We finally discuss these results in the light of mean field calculations and propose a new interpretation where quadrupolar interactions play a major role, overcoming the magnetic exchange. In this picture, the spin ice pattern appears shifted up to finite energy because of those new interactions. We then propose a range of acceptable parameters for przr, that allow to reproduce several experimental features observed under field. With these parameters, the actual ground state of this material would be an antiferroquadrupolar liquid with spin-ice like excitations.
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