I'm am trying to prove that a partial function is only computable by a Unlimited Register Machine iff it is computable by a standard TM. How should approach this proof. Does it have anything to do with reductions?

Thanks in advance

Just show that you can simulate a TM on a URM. That means a URM can run anything a TM can run, because it can just pass the input through the TM.

Then show that you can simulate a URM with a TM. This shows the same thing in the other direction.