For a quick evaluation for sulfate, you can use paper strips as mentionned in the previous answer or use colorimetric method such as visocolor product : https://fr.vwr.com/store/product/26665373/colorimetric-rapid-tests-sulphate-visocolor-eco.
Similar visocolor products also exist for nitrate ion, it working well for nitrate but the meausrements can be disturb by the presence of nitrite ion NO2-.
You also can use this product as reagent for colorimetric measures with a spectrophotometer after calibration with known concentration samples.
Hovewer we only test in water, i don't know the validity of this method on urine according to the absorption spectra of urine before colorimetric test. It will be possible if there is a wavelength shift between urine and colorimeter absorption.
Depending on how often you do this and how much money you have available, there are of course commercial kits available. But then you will have to buy both a specific spectrophotometer from the same company and the test kits.
Maybe have a look around in your university? It is quite possible, that someone already has the setup and you just need to buy the kit and you can use their machines.
Sulfate ions absorb in the range 200-220 nm (however, it depends on your matrix!!). However, the best way is the turbidimetric method using barium ions (Ba2+) to form insoluble barium sulfate (BaSO4). Then measured by spectrophotometer (proportional to the turbidity).
Edzani Mukonazwothe you didn't mention your matrix/sample.