According to VanderKam and Flint in The Meaning of the Dead Sea Scrolls ("V&K"), there are four categories of Dead Sea Scroll readings, those that follow the "Hebrew Bible", that is, those that follow what became the Masoretic Text, those that follow the Septuagint, those that follow the Samaritan Pentateuch, and, finally, "variant readings." Variant readings, then, in the Dead Sea Scrolls of Old Testament scripture are readings that are different from all three of the sources extant before the discovery of the Scrolls. At page 115, V&K write:
Some of the variant readings in the [fourth Qumran cave's first Samuel manuscript] involve individual words, phrases, or even entire sentences that were left out of the Masoretic Text or added as supplementary material. The most dramatic example occurs in [that manuscript] at the end of 1 Samuel 10, where an entire paragraph that was missing from our Bibles for two thousand years has now been restored in the New Revised Standard Version, published in 1989. (The existence of the passage was already footnoted in the New American Bible of 1970). This paragraph describes the atrocities perpetrated by King Nahash of the Ammonites, and thus explains his otherwise unusual behavior in the first two verses of Chapter 11.[My bold.]
My NET Bible (First Edition) does not have this variant reading in the text, as the NRSV has, but it is discussed extensively and sympathetically in footnote 4 at the end of 1 Samuel 10:27. (The present online edition of the NET Bible doesn't refer to the matter, as far as I can tell.) I would have liked to have been in Dallas when the translators hashed this one out. The footnote states in part: "This [variant] reading [from the subject manuscript] should not be lightly dismissed; it may in fact provide a text superior to that of the MT and the ancient versions . . . "
My 1995 The Contemporary English Version does not have the variant reading. My NIV Study Bible (Zondervan 1995) makes no mention of the variant reading anywhere.
Eugene H. Peterson, however, in The Message: The Bible in Contemporary Language (NavPress 2002) includes it. See the last three sentences of his Chapter 10 of 1 Samuel. Way to go Dr. Peterson!
My New King James Version does not have it (my edition is copyright 1982).
Here is the variant as translated in footnote 4 to 1 Samuel 10:27 in the NET Bible (First Edition):
Now Nahash, king of the Ammonites, had been grievously oppressing the Gadites and the Reubenites. He would gouge out the right eye of each of them and would not grant Israel a deliverer. No one was left of the Israelites across the Jordan whose right eye Nahash, king of the Ammonites, had not gouged out. But there were seven thousand men who had escaped from the Ammonites and had entered Jabesh-gilead.