Your question is incomplete because you have not provided the underlined pronoun. Thus, the complete sentence is the following:
Nathan told Nadir that his 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.
Step-by-step 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.