You can try like below:

Controller:

   public class PartialController : Controller
    {
        public IActionResult PartialViewFromButtonClick()
        {
            return PartialView("_PartialViewFromBtnClick");
        }
    }

Partial View Sample:

<h4>Load Partial View</h4>



<style>
    table {
        font-family: arial, sans-serif;
        border-collapse: collapse;
        width: 100%;
    }

    td, th {
        border: 1px solid #dddddd;
        text-align: left;
        padding: 8px;
    }

    tr:nth-child(even) {
        background-color: #dddddd;
    }
</style>

<div>
    <table class="table-bordered ">
        <tr>
            <td><strong>Search</strong></td>
            <td>
                <input type="text" name="searchkey" class="form-control" placeholder="Enter Search Key" />

            </td>
            <td>

                <input type="submit" value="Search" style="font-weight: bold;" />
            </td>
        </tr>


    </table>
</div>
<br />

The View Where You Like To Load The Partial View:

HTML:

 <div>
        <button id="btnLoadPartialView" class="btn btn-primary">Load Partial View</button>
 </div>

<div id="loadPartailView">

</div>

Script:

@section scripts {
    <script src="https://ajax.aspnetcdn.com/ajax/jQuery/jquery-3.2.1.min.js"></script>
    <script>
        $(document).ready(function () {
            $("#btnLoadPartialView").click(function () {
                $("#loadPartailView").load("/Partial/PartialViewFromButtonClick");
            });
        });
    </script>
}

Output:

Note: If you would like to laod partial view with parameter you could try like this $('#loadPartailView').load('/PartialController/PartialViewFromButtonClick?parameter=2095'); Additionally each time when you would load the partial view in this fashion it will autometically refresh the partial view itself. No additional things to implement.

Hope it would help you.