The correct option is A than
A subordinate clause ("he had hoped") depends on the main clause ("He performed better") for its full meaning. To combine these as one sentence, a subordinating conjunction is used. The underlined word 'since' is used for time-related and cause-related sentences depending on its context, whereas the given sentence is a comparison, "better" is a comparative adjective so we know the sentence is a comparison. Hence, 'since' is not used here, option D is incorrect. 'Than' is a comparative conjunction which is used in sentences in the comparative degree of comparison, hence it's the correct conjunction, option A is correct. 'And' and 'but' are coordinating conjunctions used when the clauses in a sentence are independent and are both complete in meaning, whereas the given sentence has a dependent clause. So a coordinating conjunction is not required and options B and C are incorrect.