The MT for Psalms 60:6 corresponding to the Christian versing 60:4 is:
נָתַתָּה לִּירֵאֶיךָ נֵּס לְהִתְנוֹסֵס מִפְּנֵי קֹשֶׁט סֶלָה
There is a problem in the MT that causes the translation problem. It is in the word קֹשֶׁט, koshet, in bold above. The normal spelling of "bow", keshet is קשת, that is, the last letter is tav, ת. But in this verse we see that the last letter is tet, ט, like the Aramaic word for "truth", kshot.
Now the Hebrew letters tav and tet are similar. In fact, in Modern Hebrew there is no distinction between them in vocalization. In traditional vocalizations such as the Yemenite Jewish vocalization, there is still a clear distinction, but that distinction is not apparent to Western listeners. The difference is the placement of the tongue when making the "T" sound. With tav, the tip of the tongue is held between the front teeth. With tet, the "T" sound is made while the tip of the tongue is pressed against the gums just above the front teeth. The tet sound is harder and shorter than the tav sound, although to Western ears they both sound like "T".
Furthermore, there are some clear cases of alternative spellings involving tet and tav in the MT, in words such as תעה and טעה.
So in this verse, קֹשֶׁט is either an alternative spelling for "bow", kesheth, or it is an Aramaic loan word for "truth", kshot. Therefore, the interpreter and translator needs to use the context of the previous and following verses to try to understand the probable meaning of the verse and decide which of the alternative understandings of קֹשֶׁט is closest to this intent.
There are two interpretation traditions of this verse. The first sees this verse as a continuation of the previous verses of tribulation, so they translate "bow", and the intent of the verse is to say "You only left your faithful followers with their flag standard on a hilltop against the bows of their enemies", like in Isaiah 30:17 (NIV):
A thousand will flee at the threat of one; at the threat of five you will all flee away, till you are left like a flagstaff on a mountaintop, like a banner on a hill.
The second tradition of interpretation sees this verse as the start of the salvation described in the following verse and read this verse as "You gave your faithful (those who fear you) a standard to rally them and you gave them your truth.
The second (NKJV) tradition sees קֹשֶׁט in this verse as corresponding to קֹשְׁטְ in Proverbs 22:21
לְהוֹדִיעֲךָ קֹשְׁטְ אִמְרֵי אֱמֶת, לְהָשִׁיב אֲמָרִים אֱמֶת לְשֹׁלְחֶיךָ
This verse from Proverbs is the basis for the prevailing Jewish interpretation of Psalms 60:4, which explains why the the KJV opted for this translation, as the KJV in general rarely differs from the rabbinic interpretation of the time.
My own preference is for the first tradition like the ESV, because it is more down-to-earth, in keeping with the outlook of the early OT, whereas the second tradition (NKJV) is a figurative and spiritual salvation the is less physical and national, and is therefore too modern to fit well in the OT context.