Context. Most well-resolved disks observed with the Atacama Large Millimeter/submillimeter Array (ALMA) show signs of dust traps. These dust traps set the chemical composition of the planet-forming material in these disks, as the dust grains with their icy mantles are trapped at specific radii and could deplete the gas and dust at smaller radii of volatiles. Aims. In this work, we analyse the first detection of nitric oxide (NO) in a protoplanetary disk. We aim to constrain the nitrogen chemistry and the gas-phase C/O ratio in the highly asymmetric dust trap in the Oph-IRS 48 disk. Methods. We used ALMA observations of NO, CN, C ₂H, and related molecules in the Oph-IRS 48 disk. We modeled the effect of the increased dust-to-gas ratio in the dust trap on the physical and chemical structure using a dedicated nitrogen chemistry network in the thermochemical code DALI. Furthermore, we explored how ice sublimation contributes to the observed emission lines. Finally, we used the model to put constraints on the nitrogen-bearing ices. Results. Nitric oxide (NO) is only observed at the location of the dust trap, but CN and C ₂H are not detected in the Oph-IRS 48 disk. This results in an CN/NO column density ratio of <0.05 and thus a low C/O ratio at the location of the dust trap. Models show that the dust trap cools the disk midplane down to ∼30 K, just above the NO sublimation temperature of ∼25 K. The main gas-phase formation pathways to NO though OH and NH in the fiducial model predict NO emission that is an order of magnitude lower than what has been observed. The gaseous NO column density can be increased by factors ranging from 2.8 to 10 when the H ₂O and NH ₃ gas abundances are significantly boosted by ice sublimation. However, these models are inconsistent with the upper limits on the H ₂O and OH column densities derived from Herschel PACS observations and the upper limit on CN derived from ALMA observations. As the models require an additional source of NO to explain its detection, the NO seen in the observations is likely the photodissociation product of a larger molecule sublimating from the ices. The non-detection of CN provides a tighter constraint on the disk C/O ratio than the C ₂H upper limit. Conclusions. We propose that the NO emission in the Oph-IRS 48 disk is closely related to the nitrogen-bearing ices sublimating in the dust trap. The non-detection of CN constrains the C/O ratio both inside and outside the dust trap to be <1 if all nitrogen initially starts as N ₂ and ≤ 0.6,