The correct option is C started
'It's high time' is an expression used to make suggestions, when one feels that it's already late for something to happen. In such sentences, the simple past tense form of the verb is used to talk about the present or future. In general, simple past tense can be used to talk about the present/future in phrases with time.
Option B: 'Started' is in the simple past tense and is used in sentences beginning with 'It's high time' to refer to the present time. Hence B is the correct option.
Option A: 'Starts' is a simple present form, just like the underlined verb "start". The only difference between the two is that the former is used for third person 'he/she starts' whereas the latter is used for first and second person: I, you, etc. Since it's in the present tense, it isn't required here. Hence A is incorrect.
Option C: 'Have started' is in the present perfect tense. It means that an action has just been completed.
Option D: Similarly, 'had started' is in the past perfect tense and states that an action has completed in the past. But, the given sentence does not state a completed action. The speaker intends to make a suggestion.
Hence options C and D are incorrect.