I've met Christians, both lay and clergy alike, who have claimed that time will cease to exist once we enter eternity at the second coming of Christ. Indeed, I held such a view myself for many years. I imagine that we are largely influenced by some of our hymnody. For example, one well-known tune speaks of the day the day when "time shall be no more." I also suspect that we are influenced by dualistic platonic philosophy that has seeped into popular culture pitting this world of time, space, and matter against the next world of purely spiritual existence. Whatever the reasons, though, we would do well to turn to the scriptures for our answer to questions like this.
When we do turn to the scriptures, the concept of time seems present in the first clause of the first verse of the first book of the Bible: "In the beginning." The notion of beginning is incomprehensible apart from the concept of time. As we proceed through the opening chapter of scripture, we find that time is present repeatedly. There is evening and morning that mark the days of the first week. Indeed, five of these evening and morning cycles pass before human beings are created on the sixth day, and an untold number of these daily cycles pass before sin and corruption ever enter the picture in Genesis 3. It would seem clear that time and linearity are part of God's pristine creation upon which he pronounced his approval of "very good." If time is part of God's original and good creation made for human beings to inhabit, I see no reason why we should suspect that time will ever be done away with. We must conclude, regardless of one's interpretive approach to Genesis 1-2, that time is said to precede humanity and, by chronological necessity, human sin. Time is not a sinful and wicked perversion of God' creation; it is, rather, a part of God's original creation that is presently in need of redemption.
Moving from original creation to the vision of new creation in Revelation 21-22, we find evidence that time is brought forward into the new earth. After the return of Christ and the consummation of his kingdom, it is said, in Revelation 22:2, that the tree of life produces fruit twelve times a year (or monthly), a truly astounding vision for those who've made a life in agriculture. This text would seem to clearly indicate that linearity has been given a place in new creation as well. Time is not to be cast off; it is to be renewed.
Let me be clear. I'm not proposing that our experience of time in the new earth will be exactly as it is in the present. Like all creation, time is eagerly expecting its freedom from bondage to decay into the glory of the liberty of the sons of God. Like all creation, there will be both continuity and discontinuity between our present experience of time and our future experience of time in the new creation. Whatever that turns out to be like, scripture seems clear that things will forever be moving forward in a measurable linearity. We can conclude then that through and through the biblical vision of the original pristine creation, the present fallen creation, and the future and eternal new creation is marked by the presence of time.
NB: I must give credit where credit is due. The first person to introduce this notion of eternal time to my thinking was my friend John S. So, thanks to him for pushing me to take account of the biblical material rather than be misshaped by popular music and bad philosophy.