1986 volvo 760 turbo shifts hard into 3rd gear. Has auto-trans. If I let up on gas then it shifts.

All automatic transmission models in 1985,1986 and onwards used either a ZF series transmission or an AW7x transmission. In either instance, shifting is accomplished by the cable at the throttle body, connected to a cam inside the transmission case. Since no brake bands and only clutch packs are utilized, it's important to keep the fluid changed according to the manufacturer's Specifications. First, have the oil serviced and screen changed. At the same time, remove the magnets and clean them of shavings. Then, adjust the cable so that it is very nearly slack on the throttle stop. This is accomplished by moving the cable adjusting jam nuts back and forth. Shortening the cable increases the shift map for shorter, harder shifts and vice versa; though it is important to ensure the crimp at the cable sheath is approximately 1mm away from the sheath end. Remember that this system is controlled by this cable and the internal governor inside the transmission case. Letting up on the gas allows the cable slack to allow the governor to increase the line pressure, allowing this car to shift to 3rd gear.

Early model ZF series are rather fragile, AW70 and AW71 series are more robust, and AW72 series transmissions are among the most stout in production at the time. Always ensure that the transmission fluid is normal in color, at the appropriate level and not full of contaminates. Do not make these adjustments until the transmission service has been completed, since there is a possibility of damage to the transmission valve body with an over adjusted cable.

To service, remove the transmission oil pan after draining the fluid. It could be hot, so ensure safety comes first to aviod burns. Remove the filter/screen. Remove the gasket and all traces of it on the sealing faces, ensuring that you do not scratch the facings on the case or the oil pan. Attached inside are several magnets, which can be removed for cleaning. They are there to catch shavings from the machining operations before they can damage the transmission. Install a new filter/screen, gasket and finally the oil pan. Install the bolts loosely and tighten only to the Specifications - overtightening will ruin the gasket and possibly damage the oil pan. Fill the transmission with the proper transmission fluid (Mercon/Dexron IIe per the transmission - see specs first) and check the fluid level, adding and topping off a little at time. Always check the fluid level on flat, level ground, passing through each gear range and waiting two minutes, cold or hot.Do not overfill, as this could damage the transmission or cause fluid to be ejected from the filler tube. Then perform the cable check, taking care to not overtighten it or else the cam will never fall against the stop. Test drive the vehicle at the end, making fine adjustments as needed.