The correct way to write this sentence is as follows,
Your brother is the newest member of the team.
C. Your is the correct answer.
A. is wrong because you wouldn't say, yours brother.
B. is wrong because yours should never have an apostrophe.
D. is wrong because you're is a contraction for, you are. And you wouldn't say 'you are brother' is the newest member.
Hope this helps. :)
