How to open link in Device browser when click on webview in xamarin forms iOS

I think you can try to achieve this by using a WebViewRenderer. Create a WebView like MyWebView in forms and implement renderers on each platform.

On iOS:

[assembly: ExportRenderer(typeof(MyWebView), typeof(MyWebViewRenderer))]
namespace OpenUriDemo.iOS
{
    public class MyWebViewRenderer : WebViewRenderer
    {
        protected override void OnElementChanged(VisualElementChangedEventArgs e)
        {
            base.OnElementChanged(e);

            if (NativeView != null)
            {
                ((UIWebView)NativeView).Delegate = new MyWebViewDelegate();
            }
        }
    }

    public class MyWebViewDelegate : UIWebViewDelegate
    {
        public override bool ShouldStartLoad(UIWebView webView, NSUrlRequest request, UIWebViewNavigationType navigationType)
        {
            if (navigationType == UIWebViewNavigationType.LinkClicked)
            {
                UIApplication.SharedApplication.OpenUrl(request.Url);
                return false;
            }
            return true;
        }
    }
}

On Android:

[assembly: ExportRenderer(typeof(MyWebView), typeof(MyWebViewRenderer))]
namespace OpenUriDemo.Droid
{
    public class MyWebViewRenderer : WebViewRenderer
    {
        public MyWebViewRenderer(Context context) : base(context)
        {

        }
        protected override void OnElementChanged(ElementChangedEventArgs<Xamarin.Forms.WebView> e)
        {
            base.OnElementChanged(e);
            Control.SetWebViewClient(new MyWebViewClient());
        }
    }

    public class MyWebViewClient : WebViewClient
    {
        public override bool ShouldOverrideUrlLoading(Android.Webkit.WebView view, string url)
        {
            if (url != "Your First Request Url")
            {
                Intent i = new Intent(Intent.ActionView);
                i.SetData(Android.Net.Uri.Parse(url));
                Xamarin.Forms.Forms.Context.StartActivity(i);
                return false;
            }
            return true;
        }
    }
}

Use MyWebView to load your url in Forms.

Use Device.OpenUri and pass your URL.

Device.OpenUri(new Uri(request.Url));

You can use UIApplication.SharedApplication.OpenUrl, but you should create a new NSUrl object, passing in your URL.

UIApplication.SharedApplication.OpenUrl(new NSUrl(request.Url));