No over drive - 1990 Volvo 740

If you have a manual transmission model, check the wiring to the overdrive solenoid (M46,M47 transmission with type M overdrive) and check all fuses. This solenoid simply opens a check valve that allows the overdrive to function (DO NOT reverse the vehicle with the overdrive engaged or damage will result to the unit itself).
Automatic transmission models also have an overdrive override solenoid, bottom left side. If it is stuck in the override mode, check for shorted wiring to the solenoid. Also check the switch which can bind closed. If you can put a voltmeter on the wiring to the solenoid itself, check for voltage; if you have voltage and the switch is known good, the wiring is faulty. No voltage means the solenoid plunger is stuck down. Remove the solenoid and repair or replace it. In most cases replacement of a well-used item is better than repair.
All models: Always verify the condition of the wiring and connectors before condemning the unit. In most cases a voltmeter will rule out what the solenoid isn't doing. If you have voltage at the terminals on manual transmission models but no overdrive function, the solenoid has either seized or the coil has burned out. On automatic transmission models voltage at the terminals means the opposite: the solenoid will override overdrive and keep it in the third gear. No voltage for manual means no overdrive; no voltage on the terminals for automatic models means overdrive engages normally; if this is the case, replace the solenoid.
If, after all this checks out, on automatic models, this means that the transmission valve body has plugged up with deposits. For manual models, it means roughly the same (the overdrive is essentially a one-gear automatic transmission) and it also indicates that something is amiss with the hydraulic circuits, in both cases. Low line pressure can also cause this to happen in both types which means either the fluid is bad, the valve body is dirty, the screen is clogged or the main oil pump in the transmission (automatic models) is leaking. Always perform a thorough check before condemning either transmission type - they are conventional in design and very sturdy.
On AW-7x transmissions, no brake bands are used, therefore only clutch packs are employed. On the M46 and M47 manual models, the overdrive is a bolt on unit (type J or type M, depending on year). On the ZF series of automatic transmissions, the overdrive is integral to the transmission, being a true fourth gear. All models use a solenoid to control the upper gear range.
Note also that if you have the manual transmission, it may prove risky to rebuild it if you can beat the synchro by a quick change. Rebuilds offer up different wear surfaces to the case and can make a noisy transmission noisier.
Automatic models utilize clutch packs front to back. Band brakes were eliminated entirely, and when these start to fail the most noticeable problem is sloppy, hard shifting even after a fluid and screen job. The clutch wear surfaces decrease in friction holding and become thin. This implies loose clutches and this implies poor shift quality.
Always change the fluid completely (including the oil cooler, note it is thermostatically controlled) and clean the magnets of all debris. Introduce new oil into the system and test again.