The correct option is A Our lead actor has fallen sick, nevertheless we shall continue with the play.
A compound sentence is made up of two independent clauses, which are
complete sentences on their own. Adversative compound sentences contain
two ideas that contrast each other in meaning. The conjunctions used in
such sentences include but, yet, still and so on.
Option A uses the adversative conjunction 'nevertheless' which refers to the contrast; it means 'in spite of that', which is apt for the sentence (in spite of the lead actor falling sick, they still continued on with the play). Hence option A is correct.
Option B is incorrect because 'since' is used in reason-related sentences; here they don't express reason, but contrast. Moreover, 'since' is a subordinating conjunction.
Option C uses the illative conjunction, which refers to one clause which is concluded or inferred from another. The second sentence doesn't express inference, hence C is incorrect.
Option D is incorrect because the answer lies in A.