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We report a uGMRT detection of HI 21-cm absorption associated with the radio source 8C 0604+728, at $z = 3.52965$. The source is at the highest redshift at which associated HI 21-cm absorption has been discovered to date, surpassing earlier known absorber at $z \approx 3.39$. We estimate ultraviolet luminosities of $\rm (3.2 \pm 0.1) \times 10^{23} W \ Hz^{-1}$ and $\rm (6.2 \pm 0.2) \times 10^{23} W \ Hz^{-1}$ , and ionising photon rates of $\rm (1.8 \pm 0.1) \times 10^{56} s^{-1}$ and $\rm (5.0 \pm 0.1) \times 10^{56} s^{-1}$, using data at different epochs; the source shows year-scale variability in both its luminosity and photon rate. The luminosity and photon rate at later epochs are $\approx 6.2$ and $\approx 1.7$ times higher than thresholds suggested in the literature above which all the neutral hydrogen in the AGN host galaxy is expected to be ionised. The detection demonstrates that neutral hydrogen can survive in the host galaxies of AGNs with high ultraviolet luminosities. We estimate a high equivalent width ratio of $15.2$ for the $\rm Ly α$ and HeII emission lines detected in the optical spectrum, that is consistent with AGN photoionisation models. However, a significant contribution from young stellar populations to the excess $\rm Ly α$ flux cannot be ruled out.