<div id="ajaxIT">
            @Html.Partial("AddRepField", Model)
        </div>
            <input type="submit" name="Add" value="add" class="btn-sm btn-default"  />}

public ActionResult Add(EventDetailsViewModel viewModel)
    {
        if (viewModel.Event.Repertoires == null)
        {
            viewModel.Event.Repertoires = new List<Repertoire>();
        }
        viewModel.Event.Repertoires.Add(new Repertoire());
        return PartialView("AddRepField", viewModel);
    }

<script src="~/Scripts/jquery.unobtrusive-ajax.min.js"></script>

<script src="~/Scripts/jquery.unobtrusive-ajax.js"></script>

@using (Ajax.BeginForm("Add", "Repertoire", new AjaxOptions { UpdateTargetId = "ajaxIT" })) {
  ...
}