It's clear they are honest.
vs.
It's clear that they are honest.
Is there a difference? Is one more correct than the other?
It's clear they are honest.
vs.
It's clear that they are honest.
Is there a difference? Is one more correct than the other?
In your sentence
It's clear that they are honest.
that is used as a conjunction to introduce the clause that serves as the complement of the predicative adjective clear.
This is one instance when that can be omitted [there are other cases of omissibility of that but I will only deal with the particular case about which you are asking]:
Adjective + that-clause
We use be + adjective + that-clause to express opinions and feelings. Some adjectives commonly used in this way are sure, certain, right, important, afraid, pleased, sorry, surprised, worried [and we can add clear in this category]. We can omit that with no change in meaning:
- It’s important (that) we look at the problem in more detail. (Cambridge)
The omission of that is still controversial nowadays, especially in writing. Many advocate that omitting that is informal, but we are seeing a shift in use even in formal speech or written texts. This site recommends:
As a general rule, if the sentence feels just as good without the that, if no ambiguity results from its omission, if the sentence is more efficient or elegant without it, then we can safely omit the that.
In your case both versions of the sentence are correct, but since there is no ambiguity and the sentence definitely feels less heavy without that, I would use
It's clear they are honest.
without any worry that the meaning is changed.
There is a difference, and that is only one of formality. Whereas the conjunction is kept in formal writing, in everyday speech it is most times dropped. The meaning remains the same. The relative pronoun "that" is also dropped similarly. Nevertheless, "that" can't be dropped in all cases.
PEU No 560 that: omission
We can often leave out the conjunction that, especially in an informal style.1 indirect speech
That can be left out informally after many common reporting verbs.
♦ James said (that) he was feeling better.
♦ I thought (that) you were in Ireland.
That cannot be dropped after certain verbs (e.g. reply, telegraph, shout) and is not usually dropped after nouns.
♦James replied that he was feeling better.
♦James replied that he was feeling better.
♦James replied he was feeling better.
♦James replied that he was feeling better.
♦ He disagreed with Copernicus' view that the earth went round the sun.
(NOT …Copernicus' view the earth went…)2 after adjectives
We can use that-clauses after some adjectives. That can be left out in more common expressions.
♦ I'm glad (that) you are all right.
♦ It's funny (that) he hasn't written.3 conjunctions
That can be left out in an informal style in more common two-word conjunctions, such as so that, such … that, now that, providing that, provided that, supposing that, considering that, assuming that.
♦ Come in quietly so (that) she doesn't hear you.
♦ I was having such a nice time (that) I didn't want to leave.4 relative structures
We can usually leave the relative pronoun that when it is the object in a relative clause.
♦ Look! There are people (that) we met in Brighton.