The correct option is
D work
In order to fill in the blank with the most suitable form of infinitive, we need to understand the meaning and usage of 'sooner than'. 'Sooner than' means the same as 'rather than', which also means 'instead of' or preferring someone or something over the other. If 'sooner than' is used in a passive (voice) sentence, we use the word 'to' along with the verb. In an active sentence, we do not use 'to' with the verb. The verbs without the marker 'to', are called bare infinitives.As the given sentence is in active voice, we will use the bare infinitive here.
Option B - 'To work' can't be used here as the verb in its original form with the marker 'to'. As the sentence is in active voice, we can't use the infinitive with 'to' here. Hence, option B is incorrect.
Option C - 'Had worked' is used to represent a sentence or an action in past perfect tense. As we need the verb in its original form, we can't use 'had got' here. Hence, option C is incorrect.
Option D - 'Have worked' is used to represent the present perfect tense. As the verb is not in its original form, we can't use 'have worked' here. Hence, option D is incorrect.
Option A - 'Work' is a verb in its original form and is a bare infinitive. Hence, option A is the correct answer.
'I would sooner resign than work more.'