The correct word to complete the sentence 'Hardly had he arrived _____ it started raining' is 'when'. This sentence structure uses a specific grammatical construction known as an inversion, often employed with adverbs like 'hardly', 'scarcely', and 'no sooner' to emphasize the immediate sequence of two events. When 'hardly' or 'scarcely' introduces a sentence, it is followed by an inverted subject-verb order (e.g., 'Hardly had he arrived' instead of 'He had hardly arrived'). The second clause, which describes the subsequent event, is then introduced by 'when'.
Similarly, if the sentence began with 'No sooner', the connecting word would be 'than' (e.g., 'No sooner had he arrived than it started raining'). The options 'than', 'then', and 'as' are incorrect in this context. 'Than' is used with 'no sooner', 'then' indicates a sequence but not in this specific inverted structure, and 'as' implies simultaneity or cause, which doesn't fit the immediate succession emphasized by 'hardly'. Understanding these correlative conjunctions is key to mastering advanced sentence structures.