Dispensationalists believe that in the secret rapture, believers will receive their new, glorified bodies. This rapture occurs prior to or during the tribulation, meaning that the current earth will continue, and only later will the new earth be made.
Dispensationalist John MacArthur, while discussing 1 Thessalonians 4:16–17 and what he believes is its teaching of a secret rapture, says:
It’s at that moment that the transformation takes place. We who are alive and remain are here and all of a sudden we’re snatched in the moment, in the twinkling of an eye. [...] In a moment, we’re transformed into a glorified body like the resurrected body of Christ. (source)
MacArthur here uses the language of 1 Corinthians 15:52, as he and other dispensationalists believe that that passage also refers to this secret rapture:
in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised imperishable, and we shall be changed. [ESV]
For example, Thomas Constable writes:
The fact that Paul included himself, in the group living at the time of the Rapture, shows that he expected that event to take place imminently. [...] The dead will rise in bodies that are not subject to corruption, and the living will receive immortal bodies, too. (source)
This understanding is also expressed by the Moody Bible Commentary and is the typical view dispensationalists: believers will be taken up (raptured) prior to final judgment, and at that time will receive their glorified bodies.
With respect to the timing of the new earth, Constable writes:
The "new earth" and "new heaven" will come into existence after the Millennium and the Great White Throne judgment. (source)
That is, following the secret rapture, the literal 1000-year reign of Christ on earth, and the final judgment, the new earth will be made. John MacArthur concurs:
Following the Lord's return, following the defeat of Antichrist, following the banishment of Satan at the beginning of the Kingdom, following the Kingdom, following the release of Satan and his destruction, following the Great White Throne comes the new heaven and the new earth. (source)