Hey,
Add the script reference in layout
<script href="@Url.Content("~/Scripts/jquery.unobtrusive-ajax.min.js")" type="text/javascript"></script>
And add Ajax.ActionLink as follows in your case.
Ajax.Actionlink("linkText","GridViewPartial","ControllerName",new{},new AjaxOptions(){UpdateTargetId="DivId",InsertionMode = InsertionMode.Replace})
Dam sure this will help. ;)