Is it necessary to use 'then' in the second/main clause of a conditional sentence?

If there is a problem, you need to communicate it.

vs.

The question is that is there a difference between the two phrases? If yes, then what is it?

Both of them seem correct. So what is the rule here (in proper/standard English Grammar)?

Short answer

There is no requirement to use then in conditional sentences at all.

There has been a lot of work carried out on the meaning of this word in conditionals, but none of it has been very conclusive. Here is a post I wrote for Philosophy Stack Exchange on the subject:

Other answer

Then is not really a logical connective at all. It is used in conditionals, but it is just an adverbial discourse marker. What it seems to show is that the speaker is prepared to assert what's coming next on the basis of whatever it is that then is referring back to as being the case. It doesn't only occur in conditionals:

• A: I'm leaving on Tuesday. B: Then you're going to miss the party.
• You shouldn't do that, because you'll then be open to accusations of plagiarism.

Notice that there are no sentences in which the inclusion or omission of the adverb then makes any difference whatsoever to the truth conditions of the sentence. In the Original Poster's question the sentence has exactly the same truth conditions whether or not then is omitted:

• If there is a problem, you need to communicate it.
• If there is a problem, then you need to communicate it.

The fact that adding or omitting then can never change our assessment of whether a conditional sentence was true, is evidence of the fact that it is not actually a logical connective. It merely adds a higher order comment about the speaker's attitude to a proposition.

Probably the best known work on the use of then in conditionals is by Sabine Iatridou On the contribution of conditional THEN. However, readers beware, the grammaticality judgements therein are, in my opinion, rather suspect in several places.

Iatridou pointed out that we are most likely to use then when we would not expect Q to happen unless P. There are many other interesting observations as well.

In short, however, then is not a logical connective at all.