You have to consider yoir audience in order to decide wht type of writing you're going to do, possibly what arguments to make, and what style you write your piece in. who you are writing for really makes your writing what it is.
Your question is incomplete because you have not provided the underlined pronoun. Thus, the complete sentence is the following:
Nathan told Nadir that <u>his</u> nerves would impact the horse's ability to carry them through the competition.
Answer:
Case: nominative
Reference: ambiguous
Sentence rewritten: After seeing that Nadir was nervous, Nathan told him that nerves would impact the horse's ability to carry them through the competition.
Explanation:
The possessive adjective his functions as nominative case because the noun phrase his nerves functions as the subject of a verb. Besides, it creates ambiguity because it is not clear whose nerves it refers to - Nathan or Nadir's. As a result, it is necessary to rewrite the sentence to clarify whose nerves affect the horse's performance.