Using DataAnnotation localizer in your extension method for HtmlHelper in ASP.net core mvc 3.1

You just need to get a reference to IStringLocalizer.

In your startup:

public void Configure(..., IStringLocalizer stringLocalizer) // ASP.NET Core will inject it for you
{
    // your current code
    YourExtensionsClass.RegisterLocalizer(stringLocalizer);
}

and in your extensions class:

public static class YourExtensionsClass
{
    private static IStringLocalizer _localizer;

    public static void RegisterLocalizer(IStringLocalizer localizer)
    {
        _localizer = localizer;
    }

    public static string DescriptionFor<TModel, TValue>(this IHtmlHelper<TModel> self, Expression<Func<TModel, TValue>> expression) 
    {
        MemberExpression memberExpression = (MemberExpression)expression.Body;
        var displayAttribute = (DisplayAttribute)memberExpression.Member.GetCustomAttributes(typeof(DisplayAttribute), false).FirstOrDefault();
        string description = displayAttribute?.Description ?? memberExpression.Member?.Name;
        
        return _localizer[description];
    }
}

If you want more control, I'd suggest you to get some ideas from how ASP.NET Core does internally, by taking a look at the source code (method CreateDisplayMetadata).