I have a 1996 Privia which does not engage overdrive. Possible remedy

The erratic jumping in and out of overdrive (O/D) on your 2006 Terrano 3GMR with a 3.2L engine could be caused by a few different issues. Here are some possible causes and fixes:

1. Faulty speed sensor: The speed sensor provides input to the transmission control module (TCM) to determine when to engage overdrive. A faulty sensor can cause the TCM to think the vehicle is going too slow or too fast for overdrive engagement. A mechanic can test the speed sensor and replace it if necessary.
2. Low transmission fluid level: Low transmission fluid level can cause the transmission to shift erratically or not engage overdrive. Check the transmission fluid level and add fluid as necessary. If the fluid level is low, it's important to also check for any leaks that may be causing the fluid loss.
3. Worn or damaged overdrive band: The overdrive band is responsible for engaging and disengaging overdrive. If the band is worn or damaged, it may not engage properly. A mechanic can inspect the overdrive band and replace it if necessary.
4. Transmission control module (TCM) issues: The TCM controls the shifting and engagement of overdrive. If the TCM is malfunctioning, it may not engage overdrive or cause erratic shifting. A mechanic can test the TCM and replace it if necessary.

It's recommended to have a professional mechanic diagnose and repair the issue, as the transmission is a complex and vital component of the vehicle.

Use your overdrive when driving at highway speeds on long stretches of road. Disable your overdrive (turn it off) when driving in the mountains and when towing something. When driving in traffic, use your own discretion as to whether or not to use overdrive, based on the amount of start & stop driving you are doing, and if you are attaining speeds high enough for overdrive to engage (above 40 m.p.h., generally).

It means overdrive is not on any more. Overdrive is high gear, good for gas mileage, but not good where power is needed or in the hills.

check your shift solenoid (A-B-C-D), i have the same problem. OBD PO700 (Transmission Control System) , PO750 (A), PO755 (B), PO60 (C), PO765 (D). i hope this helps.

The starting issue could be due to a bad battery. Hard starting in the morning is usually associated with the cold. Low temperatures, create hard starting/cranking for your battery.
You will see a CCA rating on your battery, in my 4wd it is 600CCA that means it has 600 Cold Cranking Amps. That means it is the amount of current my battery can provide at O deg F. Car manufacturers only use cheap standard duty batteries.

If it is a 4 speed automatic with a power/ecconomy button it won't engage overdrive. You put it in ecconomy for normal driving and power for towing.

is this a three speed trans? or 4spd w/overdrive? either way i believe you have a pressure problem whether a torque converter or a trans pump. I was wondering how you know all gears worked if it will only do 30 mph as the 4th or overdrive usually wont engage at that speed. but here say,

this is really not a problem, overdrive will only be used if car speed is up to speed for it to engage and that is how its designed. If you pull a trailer or if you are in a hilly area and your car keeps shifting in and out of overdrive you should turn off untill more flater terrain, otherwise it doesn't hurt your vehicle.

The guys that know if this is possible are the wrecking yard guys. You need to call a few of them and see if it is possible. You will need the new flywheel, clutch and clutch release items.

Check for a damaged wheel rim- the wheel balancer should have detected this, but may have missed it.
Check for defective tyre- new tyres can have faults -rotate wheel while jacked off ground, look for bulges, lumps or tyre runout when rotated.
Check for looseness of tie rods and steering box etc.
Check wheel bearings are ok.

There is an electronic sensor on the outside of the transmission.Change the filter and fluid and replace sensor.The sensor costs around $150.
"High speed" probably is over drive,so if it is turned off,it can't engage.I have found that cutting the overdrive switch on and off can cause excessive wear and tear on the overdrive. 

Regardless have the car scaned for a any codes thay is causing the problem. Just trying to keep the cost of repairs down by know exactly what the ECM has in it's memory for any malfunction that is creating your overdrive from engaging.
Good luck and hope this helps