The difference is whether the word "the orchestra" needs a plural or singular verb. In American English a singular verb is needed (so American English would only accept options a) and c) ) but in British English both forms are acceptable: so in British English all four sentences are correct.
The answer to your question would be that the sentences that have correct subject-verb agreement are the following ones: "The orchestra has a new conductor" and "the orchestra needs a new conductor". That is, the correct options would be A and C.
"Orchestra" is a collective noun which American English requires to be singular.
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