Final answer:
The sentence given is a complex sentence, not a simple sentence, because it consists of one independent clause and one dependent clause.
Step-by-step explanation:
The sentence "Mayor Santiago started a successful program for young musicians after he left city politics." is not a simple sentence. Instead, it is a complex sentence because it contains one independent clause and at least one dependent clause. The independent clause is 'Mayor Santiago started a successful program for young musicians', and the dependent clause is 'after he left city politics', which provides additional information about the timing of when he started the program.