Question

that's the player ___ career was ruined by health problem​

Answer 1

Answer:

that's the player who's career was ruined by health problem.

Answer 2

"That's the player whose career was ruined by health problem​- Relative pronoun".    

Explanation :

Here we use a relative pronoun word whose to complete the sentence.

A Relative pronoun is a word that makes the sentence dependent or relative clause and links it to an independent clause.

There are five most common relative pronouns:  who, whom, whose, which, and that.

Also, two more words are sometimes considered as relative pronouns, those are whoever and whomever which used in some particular situation.