Allah says:
And We send not the messengers except as bringers of good tidings and warners. So whoever believes and reforms - there will be no fear concerning them, nor will they grieve. (6:48)
There are many other similar verses.
Someone could interpret this as meaning the good believers will never feel fear or grief either in this world or the next.
But, this interpretation would be refuted by the fact that even the prophets are known to fear some things as mentioned by Allah.
So, what we are left with is that it either refers to a specific fear or refers to a specific time.
If specific fear, it might refer to the fear that Allah will be unjust with them.
If specific time (and this is by far the most supported by the rest of the Quran and the mufassiroon), this refers to when they enter Paradise.
The reason I say it is most supported is because plenty of other verses elaborate that this fear is about in Paradise.
For example, Allah says:
[Allah will say], "Are these the ones whom you [inhabitants of Hell] swore that Allah would never offer them mercy? Enter Paradise, [O People of the Elevations]. No fear will there be concerning you, nor will you grieve." (7:49)
In this verse, Allah shows that "No fear and no grief" is said to the people of Paradise when they are entering it.
And Allah says:
[To whom Allah will say], "O My servants, no fear will there be concerning you this Day, nor will you grieve, (43:68)
In this verse, Allah says there will be no fear "this Day," implying it existed before.
In other verses, this phrase of "no fear" is mentioned after Allah mentions the reward. Like when Allah says:
Yes [on the contrary], whoever submits his face in Islam to Allah while being a doer of good will have his reward with his Lord. And no fear will there be concerning them, nor will they grieve. (2:112)
And Allah knows best.