In Jesus' interactions with the woman at the well in the Gospel of John chapter 4, we find that the one who drinks the living water Jesus gives him shall never thirst; rather, the living water will become in him a wellspring of water springing up to everlasting life.
About a decade ago, in a church in New Delhi, a preacher talked about the fact that we continue to thirst after having tasted Jesus. He clarified that this is a thirst to have more and more of Him. The church being a charismatic one, he insisted that this meant being filled with the Holy Spirit with the mystical, almost tangibly cognitive experience it brings. The assurance that we will never thirst again, he clarified, meant that we will never lack the source for the water (my paraphrasing here- I've forgotten the exact words he used).
If a non-charismatic congregation were to be asked to clarify this, they may concur that the thirst to have more of Him in their lives is persistent- they may not agree on the precise way in which they are filled with the Holy Spirit, but they would agree that the thirst is present in their struggle with sin on a daily basis, in the leading of God on important decisions, in His word that refreshes their minds and hearts.
In a magnificent passage, Jill Carattini, senior associate writer at Ravi Zacharias International Ministries, writes about the three stages of our experience with God (Second Naïveté). She writes that we initially experience the stories of creation, God's presence, provision and love as children and see God as the great adventurer who leads us through a great story, we see God at the centre of the universe, with everything else including ourselves surrounding Him. In the second stage we are clouded by the disturbing and disharmonious skepticism of the world around us which pressures us to live for ourselves, quesion God and puts us at the centre with God and others around us. The dissonance between these two stages is great as these are two different worldviews. The third stage that some of us experience is bigger than we know how to tell as God once again occupies the centre as we come to know the Person of Christ behind the Word that we came to hear as children. She writes:
Like God's response from the whirlwind to a questioning, anguished Job--"Where were you when I laid the foundation of the earth?"--we rediscover the one at the center, and it isn't ourselves. In this stage of second naiveté, the Bible can be engaged with awareness and imagination, and a greater sense of devotion, because we have come once again to see the God to whom it points.
I think this passage captures nicely the difference between the existential angst keenly felt by the skeptic (the Thirst) and the desire to know Jesus more and more (the Longing). One is a cry for help, the other is an experience of a relationship, the difference between them being profound. The renewal of our minds by God's Word and His Spirit are ongoing processes and form the wellspring of water welling up to everlasting life, in turn flowing out and quenching others' thirst as well.