The first topic for change is a new hull. The Navy wants a new hull thus eliminating the current Arleigh-Burke and Zumwalt hulls. The second item under review is stealth capability. A new cruiser may forego some stealth and rely more on combat sensor fusion from satellite to ship and defensive laser guns canceling the need for a fishing boat size of the electronic signature. The thought maybe "we are right here, come and get us" so the hull design will be based on optimal function more than having a stealth-like capability. The thought may come to, "you can't hide a carrier because we don't have to."
A cruiser may follow the carrier philosophy having systems adequate enough taking out any attack from above or beneath the surface and stealth is an expense better spent on weaponry. Speed and endurance may be the primary changes made to the cruiser. Not as many will be built as an Arleigh-Burke or LCS were built but it doesn't have to have numbers. The purpose of a cruiser may become an ocean region focal point where it manages all military assets while traveling fast looking for that opportunity to Marshall military assets. It will have a battle punch itself! Submarine warfare will have a high priority in its suite.
The hull will be designed for speed and space as the battle nerve needs to move quickly as carrier groups ply the seas. It will become the quarterback for the destroyer groups escorting a Gerald Ford class carrier. It could be the F-35 of the high seas with its own suite of sensor fusion. If you miss the battleships from WWII then buy the board game.
The Zumwalt is the pilot hole for the next cruiser. The Arleigh-Burke are the lessons learned as the battlefront changes.
Another talking point is propulsion. Could it be a nuclear-powered machine? That is a strategic question. Fossil fuels can power a ship for about ten thousand miles and then require a fill-up. If a ship is in service for 40 years that is a lot of fossil fuel that may be not around when the ship progressive through its lifetime of service. In a time of war, oil access becomes a weapon. A nuclear warship includes a bulky space for a reactor. But a mass of petroleum is no longer needed for its operation. This is a concept where better military minds can determine a direction on how to use fuel. If a cruiser is few in numbers like the carriers then there are many questions about how much the Cruiser will do in an over-arching warfare mode. Or how important the cruiser becomes because of new capabilities installed. As stated earlier complete stealth is being traded out for speed and size having weapons capabilities for neutralizing adversarial weapons. It will take another 15 years before a ne cruiser type is deployed and could be a replacement for the Destroyers with fewer numbers.