Note: This answer should not be viewed as complete in any way, security is always hard and if it's important to you - always consult with a third party security and penetration testing company. This is just a few things you should consider to make your MVC application safer (not necessarily safe).
Protect controllers
First step is to apply [Authorize] to your controllers, to make sure there is some sort of valid authentication before accessing a method. Preferably add Authorize to all controllers and make exceptions with [AllowAnonymous] to make it secure-by-default.
Authorize the user
Even though you've added [Authorize] to the controller, that only means that the user is logged in, not that the user should have access to whatever method is being accessed. The first step is to extend the attribute by specifying a set of roles for the method: [Authorize(Roles = "Administrator"]
Depending on the application, you might also have to check that the current user belongs to the company/group or whatever that is being edited, to prevent someone from modifying data that doesn't belong to them.
Don't leak data into models
If you're using your actual data models as view models, you are at risk of allowing the user to enter more data than they're supposed to. Consider this example:
class Employee {
public int Id { get; set; }
public string Name { get; set; }
public int Salary { get; set; }
}
Assume that we for some reason allow our employees to change their name, and we use the Employee model for that. But of course we only make an edit field for the Name, and not the Salary as that would be stupid :D. However, due to how the model-binding works, a smart Employee could just add <input type="text" name="Salary" value="2147483647"> to the form when changing their name, and our gullible db.Entry(employee).State = EntityState.Added; followed by db.SaveChanges() would update their salary as well.
Solution? Either make a view model with only the Id and Name property, to make it impossible to change the salary, or use the Bind attribute to only include the properties we allow: public IActionResult Update([Bind(Include="Id,Name")]Employee model).
XSS
A very important part is to protect your users from bad dynamic content. If I can enter HTML and Javascript that's displayed to some other user, I can abuse that to steal their authentication token for example. Making to never render user-entered data as HTML is a first step to prevent this. You should also make sure to always use the anti-forgery token in your forms as well. Adding CSP headers is a good practice to prevent someone from injecting scripts that shouldn't be there.
[Authorize]annotation will check against unauthenticated requests on the controller/action that it is on as well as check that a user is in a given role. As far as applicaton code goes, there are many other ways hackers can gain access to or exploit your applications (sql injection, XSS, etc) Completely protecting your application from hackers in any live, hosted environment is a much bigger topic than securing application code. I think we need more specifics on what exactly you're looking at securing or else the answer to this will be multiple entire books