Pretty sure ServiceLocator.Current is not available yet becuase it is still doing initialization.  You should use

context.Locate.Advanced.GetInstance<IContextModeResolver>

I also think you need to make sure it has been intialized by adding module dependency

[ModuleDependency(typeof(EPiServer.Initialization.CmsCoreInitialization))]

Your code example is weird. You are trying to fetch the instance of IContextModeResolver in ConfigureContainer - the method that's used to build up the service locator. It would be more reasonable to fetch that instance in the Initialize method, if anything, when the service locator is ready to use.

You have at least two options to override IContextModeResolver - either use StructureMap and For<IContextModeResolver>().DecorateAllWith<T>(...) or you can replace the registered resolver of IContextModeResolver using context.ConfigurationComplete += (sender, args) => { context.Services.RemoveAll<IContextModeResolver>; context.Services.AddTransient<IContextModeResolver, CustomContextModeResolver>(); }.

I did it exactly as Mark told above in the comments & its working perfectly fine. This is the final version of the code -> 

[ModuleDependency(typeof(ServiceContainerInitialization), typeof(EPiServer.Initialization.CmsCoreInitialization), typeof(InitializationModule))]
    public class DependencyInjection : IConfigurableModule
    {
        public static IContextModeResolver contextModeResolver { get; set; }
        public void Initialize(InitializationEngine context)
        {
            contextModeResolver = context.Locate.Advanced.GetRequiredService<IContextModeResolver>();
        }

        public void Uninitialize(InitializationEngine context)
        {
            throw new NotImplementedException();
        }

        public void ConfigureContainer(ServiceConfigurationContext context)
        {
            context.Services.AddTransient<ICorClient>(l =>
            {
                if (contextModeResolver.CurrentMode.EditOrPreview()) return new CorClientStub();
                return new CorClient(l.GetInstance<HttpClient>());
            });
}
}