Nine out of ten times a clog in the shower will mean a concentration of hair tangled in the mechanical drain assembly. This mechanism shuts the drain off when it’s down and releases the water when it is lifted up. Usually this is accomplished with a rod connected to a plunger that drops and rises with a lever attachment that protrudes into the tub.
Normally there are two Flathead screws that hold the overflow plate in place. This equipment is located below the spout and above the drain in the bathtub. If you remove the two screws the whole Assembly can be lifted out and cleaned. Remove any hair or soap scum.
Next coat the whole assembly generously with petroleum jelly. This will assure the assembly moves freely and doesn’t jam as it’s operated within the piping. It will also help the brass assembly to retard any corrosion.