Q:

cannot convert argument 1 from 'std::shared_ptr' to 'std::shared_ptr>

When trying to call a method setCurrentState Im getting the error:

StateMachine<Cow>::setCurrentState(std::shared_ptr<State<Cow>>)':
  cannot convert argument 1 from 'std::shared_ptr<ChaseState>' to
  'std::shared_ptr<State<Cow>>'

This indicates that a std::shared_ptr<ChaseState> is not a std::shared_ptr<State<Cow>> but why is it not?
The call to the function:
std::shared_ptr<ChaseState> initialState = std::make_shared<ChaseState>();
m_stateMachine->setCurrentState(initialState);

State.h
#pragma once
template <class entity_type>
class State
{
public:
    virtual void enter(entity_type*) = 0;
    virtual void execute(entity_type*) = 0;
    virtual void exit(entity_type*) = 0;
};

ChaseState.h
class Cow;
class ChaseState : State<Cow>
{
public:
    ChaseState();

    // Inherited via State
    virtual void enter(Cow*) override;
    virtual void execute(Cow*) override;
    virtual void exit(Cow*) override;
};

In my StateMachine I have private variable:
std::shared_ptr<State<entity_type>> m_currentState;

and the setCurrentState function:
void setCurrentState(std::shared_ptr<State<entity_type>> s) { m_currentState = s; }

As I understand the derived class ChaseState is a State (behause it inherits from state). 

A:

You need to declare your inheritance public. Class inheritance is private by default, meaning that you cannot cast from Derived to Base because the inheritance is not recognized outside of the class itself (same as how private members cannot be accessed outside the class).
To fix, make your inheritance public:
class ChaseState : public State<Cow>
//                 ^^^^^^

