Prelate vs. Spartan

Who would win in a fight? A San’shyuum super soldier (Prelates) or a Human Spartan?

Depends.

MC in his prime did beat the Didact twice, so I doubt he’d lose to a Prelate no matter the circumstances, but I’m not as sure about the other Spartans. I’d have to imagine the Prelates are technologically superior to Spartans, and the San 'Shyuum are the only race in the Covenant to come close to Humanity in terms of intelligence, so the Spartan is going to have a hard time outsmarting him, unless maybe the Prelate is just as blinded by religious fanaticism as all the other Covenant are.

So overall I’d say a normal Prelate beats the average Spartan 9 times out of 10, the average Spartan beats a fanatical Prelate 8 times out of 10, and MC beats any Prelate 10 times out of 10.

From what I know,Prelates are only armed with close quarter weapons so,an Spartan could simply shoot him.

Unfortunately we do not know that much about the prelates as we only have one story featuring one.
From Halopedia:
“The augmentations provided to Prelates were developed in the Sacred Promissory of High Charity and included genetic, physical, and chemical changes, as well as suits of highly advanced powered armor and intensive combat training. Prelates were capable of releasing chemicals into their bodies to enhance their combat abilities, or to attempt to control their consciousness.
Prelate armor included an anti-gravity belt that could be used to quickly propel themselves in various directions, or allow them to engage in limited flight. The armor also included a gauntlet made of hard light, which when activated produced a crescent blade on the forearm, as well as a shield of hard light to deflect shots that managed to connect with the highly mobile Prelate. Prelates were considered formidable foes, powerful enough to give even veteran Sangheili pause.
The augmentations given to the Prelates were not without risks, however. Prelate abilities were expected to be used in short bursts; pushing their bodies too far could cause sudden exhaustion, seizures, and—in rare cases—death.”

The Prelates were created the hope that they could beat Spartans, however since the two never once engaged in a fight this claim will never be proven true or untrue.
Based on Tem’s feats Prelates are very fast and he was able to match Rtas Vadume in a sword fight and eventually gain the upper hand. While this is impressive on its own, this feat could be attributed more to personal skill than augmentation.
The downside of a Prelate’s augmentation is that they don’t last long. Tem’s stamina was only able to last for one sword fight against Rtas before he hit his limit. That’s very short.

Taking into account these abilities I would say that a Prelate would be a tough fight for Spartan, but no tougher than fighting a very skilled Sangheili. I think it would ultimately come down on the personal skill of the two combatants and the context of the fight (since close quarters with a Prelate’s energy blade would put a Spartan at a considerable disadvantage).

In terms of pure physical capabilities, I would say that Spartan’s are currently better than Prelates now that they have Mark 6 and Gen 2. Ever since Spartans received these upgrades we’ve rarely seen them be matched by Elites and they are usually tossing elites left and right like canon fodder.
example: Jerome vs Elies (halo Wars 2), Locke vs Jul (Halo 5), Adrianna vs Elites (Halo Envoy) etc…