Implement interface to run a code at application Start

Define your interface and class:

interface IOnStartup
{
    void OnStartup();
}

class YourClass : IOnStartup
{
    public void OnStartup()
    {
    }
}

Add in Global.asax

public void Application_OnStart() 
{
    var cls = new YourClass();
    cls.OnStartup();
}

You cant run any code by implementing an interface you can just force your class to implement the code for OnStartup method

interface IOnStartup
{
    void OnStartup();
}

class MyClass : IOnStartup
{
    public void OnStartup()
    {
       // your code for OnStartUp method
       // you are forced to implement the code for this method because your class implement IOnStartup
    }
}

Or you can define an abstract class that implement this code and to inherit all classes that should have that method from this abstract class.

abstract class OnStartUpClass
{
    public void OnStartup()
    {
        // the code for this method
    }
}

class MyClass : OnStartUpClass
{
    // implement code for this class
    // you already have this method in your class
}

I think what you want to do is not achievable by implementing an interface. You should choose another way to do that.

If I understand you correctly, if there is a class that implements a given interface, you want that class to be instantiated and have it's OnStartup method called. If that is what you are trying to do then you have to rely on reflection.

In Application_Start call a method that will load all types present in your assembly and check if any of them implements that interface. If found you can instantiate an instance of it and call the method on that class.

If you want to add the class dynamically without recompiling your own application then it gets more complicated and involves creating AppDomains but it is also feasible.

EDIT

This question on stackoverflow tells you how to get all classes that implement an interface:

Getting all types that implement an interface

I would use an IOC container like Autofac, Ninject, Unity. Then you can register the interface with the framework and use the service locator to return all instances of classes that implement the interface.

//using Autofac
var builder = new ContainerBuilder();
containerBuilder.RegisterAssemblyTypes(Assembly.GetExecutingAssembly())
                            .AsImplementedInterfaces()
                            .InstancePerLifetimeScope();

var container = builder.Build();
var myItems = Container.Resolve<ISomeInterface>();

foreach(var item in myItems){
    item.DoSomething()
}