The correct answer is D. had got.
The sentence is in the past perfect tense, which is used to talk about something that happened before another event in the past. In this case, the event that happened before the driver turned up for extra duty is that he got a telephone call. The past perfect tense is formed with the past participle of the verb (got) and the auxiliary verb had.
The other options are incorrect because they are not in the past perfect tense. Option A, having got, is in the present perfect tense. Option B, being got, is in the passive voice. Option C, having been got, is also in the passive voice.
Here is a diagram that shows the difference between the three tenses:
Tense | Time Reference | Example
——- | ——– | ——–
Present | Now | I am driving.
Past | Before now | I drove.
Present Perfect | Before now and up to now | I have driven.
Past Perfect | Before a specific time in the past | I had driven before I got the telephone call.
I hope this explanation is helpful!