Assuming you have an AC motor and an external overload relay.
So do you have an overload relay that can be remotely reset? It is not common, but is sometimes a feature of solid state OL relays. Others that are not SS sometimes have a solenoid powered plunger that will push the reset button as well. What you have will make all the difference in how you implement it in a program.
A work-around would be to use an OL with automatic reset, then wire the Trip indicator aux to the PLC as an input, count the number of trips and after 3, YOU disable the starter control via the program and require a manual push button closure to a different input to reset it after some proscribed time. The OL relay itself will of course still automatically reset, but you will have disabled the starter elsewhere.
However, you may not get to dictate when and how often the OL relay can be reset. The trip times and cooling time constants used in OL relays are designed to mimic the thermal damage curve and cooling time constants of the motors they are connected to.