The correct option is
A Regularly
In order to fill in the blank with an adverb, let's understand what adverbs are. Adverbs are the words that explain/describe other adverbs, adjectives and nouns. For example, 'I ran quickly.' Here, 'quickly' explains the way the subject ran.NOTE: We need an adverb to describe the adjective 'intense' and the noun 'atmosphere'.
Option B - 'Regularised' is a verb. 'The government has regularised its actions.' Hence, option B is incorrect.
Option C - 'Regular' is an adjective as well as a noun. 'I take breaks at regular interval.' Here, 'regular is used as an adjective. 'Give discounts to the club regulars' - here 'regular' is used as a noun. Hence, option C is incorrect.
Option D - 'Regulate' is a verb. For example, 'They regulate the company.' Hence, option D is incorrect.
Option A - 'Regularly' is an adverb, which explains how often the actions take place. Hence, we can use 'regularly' here to describe how often Indians visit Chennai. Thus option A is the correct answer.
'Even non-resident Indians regularly visit Chennai during this part of the year.'