The Old Testament Hebrew definition of hell is different from the New Testament definition of hell. So even though you see hell in both the Old and New Testaments, they mean different things.
In the Old Testament, the Hebrew word translated hell is “sh’owl“, which means grave or the world of the dead. So when David said, “If I make my bed in hell [sh’owl], behold, thou art there“, (Psalm 139:7) it was sh’owl, a place of the dead, he was referring to.
However, the New Testament concept of hell, is different. Three different Greek words were used, which were all translated as hell in the King James Version. The main Greek word translated is “geenna“, which means a place of everlasting punishment – considered also a place of future torment. It is this geenna Jesus used in Matt 5, 10, 18, 23, Mark 9 and Luke 12. James 3:6 used same word.
The second Greek word used is “hades” (refer to Revelations 1:18) which is the equivalent of sh’owl of the Old Testament, a realm of the dead. But it also means death or grave. It was this word Jesus used in Matt 16:18 when He said, “The gates of death shall not prevail” against His church. It was this “hades” that was used throughout the book of Revelations. In Revelations 20:13, we were told that “And the sea gave up the dead which were in it; and death and hell [hades] delivered up the dead which were in them: and they were judged every man according to their works“.
The last Greek word used in the New Testament is “Tartaroo“, which also have the idea of everlasting torment for the wicked – Peter used this in 2 Peter 2:4.
So, yes, hell exist as a place of everlasting punishment for the wicked (i.e. those who don’t believe in Jesus) different from hell as a realm of the dead as described in the Old Testament.
And I think sometimes people tend to forget that both Old and New Testament weren’t written in same language. Old Testament was mainly written originally in Hebrew with few chapters of Ezra and Daniel written in Aramaic while the New Testament was entirely written in Greek, (Biblica, 2013). English is a limited language, hence all those words were translated as “hell”.