Grammatical problem

It is hard to believe that he is dead.
Q:Here, how “it” is a part of an idiomatic expression.

No. It’s one of the pseudo or literary subjects. In your example, ‘it’ means ‘believing that he’s dead’.

as the subject of an impersonal verb the pronoun(it) is not actually used in place of a noun, but is part of an idiomatic expression. My question is how it is followed in the example above?

I think you can consider it idiomatic for all practical purposes.

It is hard/easy/impossible/difficult to do something.

In informal speech, the “it is” part can be ommitted altogether, and you can say: hard to believe that he’s dead.
Keep in mind that in formal writing it cannot be ommitted though.