Was driving down road with speed control on when the engine rev up and stop moving. Engine stayed running but will not engage in to any gear what could cause this problem?

If the engine revs and you get no motion in gear, then the transmission is not engaging.

If engine revs increase but road speed does not increase, your clutch is coming to the end of its life and needs to be replaced

Is the car equipped with the Automatic Transmission?
If so, read on.
Otherwise skip to the end and answer some questions.

POSSIBLE SCENARIO:
I have observed a condition where my car surges slightly when the torque-converter clutch (TCC) cycles between lock and unlock when driving on an uphill grade.
First some basics and history that will explain why the TCC is used.

Engine, Torque Converter, TCC, and Transmission relationship--
The TCC allows for a solid connection between the engine and transmission which allows the input to the transmission to rotate at the same speed as the engine.
Without a TCC, there is slippage between the engine and automatic transmission. The slippage is greatest at low engine RPM. That is what allows the engine to run with the automatic transmission in gear, like when you first shift into gear or stop at a stop sign. When the throttle pedal is depressed, the engine RPM begins to increase and the torque converter begins to slip less and less the more the engine RPM increases. The car moves. But even at cruising speeds the torque converter slips slightly. Engine RPM is greater than transmission input RPM, which is realized as slight decrease in fuel efficiency.
When acceleration is complete and a constant speed is being maintained, the engine power output is reduced to the point where the TCC can engage and eliminate any slippage between the engine and transmission. If the car has a tachometer the engagement of the TCC can be verified when a slight reduction in engine RPM observed without a corresponding change in vehicle speed.
One method used to test the operation of the TCC is as follows:
Find a flat section of road where it is safe to perform the test.
Reach a steady speed and keep the gas pedal depressed with one foot. While observing the tachometer (or listening for an increase in engine RPM), with the other foot depress the brake pedal enough to activate the break light switch but not enough to engage the brakes. When the brake light switch activates, the TCC receives a signal to disengage. With the gas pedal being held steady, release the brake pedal and the engine RPM should decrease when the TCC engages.
Old cars with Automatic Transmissions did not use a TCC. I believe the TCC was put in use in an attempt to increase fuel economy.

MY EXPERIENCE WITH SIMILAR SYMPTOMS
The condition that causes that issue on my car is this:
- A slight uphill grade increases the load on the engine.
The car tends to gradually slow and it is necessary to depress the gas pedal to maintain speed.
- Depressing the throttle pedal (manually, or automatically with cruise control engaged) signals the torque converter clutch to unlock when the load increases slightly. (A more drastic load increase would signal the Transmission to downshift to a lower gear.) The corresponding increase in engine RPM and output is enough to compensate for the reduction in speed. When the vehicle speed, engine RPM, and throttle position stabilize to the point that the TCC will engage and the engine RPM will reduce in correspondence with TCC engagement. Now, if the road conditions have not changed, power output is not enough to maintain vehicle speed. With the increased load caused by full engagement between engine and transmission, and the cycle (surging) repeats itself until the road conditions change.

Does that help?
If not:

QUESTIONS
Please define the symptoms.
What are the road conditions when the surge occurs? (A slight uphill grade?)
What is the frequency of the surge?
Does the engine power output have a noticeable surge?
Is there a speed change related to the surge?
Does the tachometer move up and down with little or no change in vehicle speed?
Are all instrument indication in the normal range?
What else has changed?

Good luck!

I will answer this as if it is a manual gear box as the solution will be different for an automatic.
First gear has a syncro ring energise spring that when pushed against the syncro cone in the gear spins the gear to the relevant shaft speed so that engagement is smooth. Because of the vast difference of the shaft speeds when engaging 1st gear the energising doesn't get a chance to work and so the gears refuse to mesh. To possible ways to get around this is to keep the road speed low say around 10mph or less or increase the engine rpm up to around 3500-4000rpm before trying to engage 1st gear. Basically the syncro is for engaging the gear as you are coming to a stop or going very slow . Check the drain plug magnet for metal as the clutch shaft bearing may be moving forward and preventing the engagement properly.

Nothing, you have hit the rev limiter. The up and down is the computer controlling the rpm. If you drive it, it should rev past 3,000. The computer is designed to keep free wheeling rpm to that level. It will only allow a higher rpm if vehicle is in gear and moving with a load.

I’m happy to help further over the phone at https://www.6ya.com/expert/david_c087e4b7d13c0163

it may be your shift solenoids their are two of them that controls upshift #1 solenoid controls 1-2 gears then #2 controls 3-4 which transmission do you have in your suburban do you have the 4L60E OR 4L80E if you have an older suburban with a Carb on it then you will have the 700rr

One thing you haven't mentioned is if the frequency of the ticking increases with engine revs? Or does it increase with road speed? Or stay the same no matter what? If the freq increases with revs the problem is most likely to be in the top end of the engine. if it goes up with road speed, it is likely to be in the region of the final drive system. If it stays the same it is likely to be an electrically driven ancillary. I hope this will (at least) point you in the right direction.

Check gearbox oil

You have governor with a missing spring or it could be in the wrong place. If the springs are all OK then you may have a bad governor gear in the crankcase. This engine is bad about the governor gears bending the governor gear shaft.