My car’s transmission gears are very hard to shift.
Sometimes the transmission won’t shift into gear at all.
Could this be the linkage or should I replace the gearshift?
Transmissions — both automatic and manual — require that the shift linkage be adjusted properly.
This means that unless the linkage pushes with the correct directionality and pushes far enough, the transmission will not go into gear.
Also, unless the linkage is adjusted properly, it may not be shifting completely out of gear. It must shift and be clearly out of a previous gear before it will be able to extend into another gear.
Check the linkage for excess play. Check the linkage for bent levers and lost clips. Be certain that the linkage is pulling the transmission out of gear before it attempts to push it in another gear position.