What would be some common applications involving high friction and low wear rates? for example, gear-driven mechanisms which require high friction between the gear teeth but ideally low wear between them.
As mentioned in the comments you don't actually want high friction between gear teeth, the tooth profiles are designed to roll over each other indeed the ideal is to minimise any sliding friction between the teeth.
Obvious examples of devices which use sliding friction are brakes and friction clutches, these will have a limited wear life depending on the material used and in general there is a compromise between performance and life, especially for clutches which tend to be relatively difficult to replace. These devices may also also include some sort of self adjusting mechanism to compensate for wear of the friction surfaces. Often two different materials will be used with one designed to wear faster but be easier to replace eg bolt or clip on pads working against a steel or cast iron friction plate (as in disk brakes).
Another example is tyres which need to have low rolling resistance but high static friction to provide grip and traction.
Friction is also very relevant in screw threads, wear is significant for things like lead screws on lathes etc which are subject to repeated sliding friction and where it is usually desirable to keep backlash to a minimum. Also on threaded fasteners there is a conflict between wanting low sliding friction to allow consistent torque setting and reduce the risk of galling but having adequate static friction to prevent fasteners from coming undone through vibration etc while still allowing reasonable manufacturing tolerances and there are various retaining devices such as nyloc nuts, spring and serrated washers and locking compounds used to achieve this.
You could also say that cutting and abrasive operations fall broadly into this category although this is normally considered separately from conventional friction per-se. Although of course the analogy if pretty good for things like bonded abrasives and diamond coated cutting tools.
As mentioned in the comments you don't want high friction between gear teeth, but if you're asking about the materials who exhibits higher friction with low wear rate, it depends on several parameters, such as, the nature of the two counterfaces, the environment, the applied load, the hardness, velocity, etc In general there's cubic crystal oxides, with a high hardness above 10GPA whom with sliding against certain material, exhibits highr friction coefficient with a loaw wear rate, we take an example of AL2O3. Best regards