To achieve what you are expecting you will have to do a little javascript. From what I understand you don't need to send ajax request as you asked for your form to reload when it gets submitted. But I'll give you both approaches.
No AJAX
First we will add a id to your form. Here in my example it will be "my-form". And an onchange event to your select that will call myFunction();.
We must also tell to your form to post the data for your current PHP script to work or it will send it as a get
<form id="my-form" action='a.php?' method="post">
<SELECT onchange="myFunction()" name="client_id" ID="mySelect">
<OPTION value="artes>'">artes</OPTION>
<OPTION value="ingles">inglés</OPTION>
</SELECT>
<input type="submit" name="chooseclient" value="Select">
</form>
Now in a javascript file or between a script tag add your function :
<script>
function myFunction(){
document.getElementById("my-form").submit();
}
</script>
Now your form should submit itself when you change the value of your select. BUT you will have another problem.
if(isset($_POST['chooseclient'])){
$clientid = mysqli_real_escape_string($mysqli, $_POST['client_id']);
//MYSQL query here
}
When you submit a form via javascript, your submit button will not be sent with the rest of the data. so if(isset($_POST['chooseclient'])) will never be true. To tackle this you have a few options, I'll give you two :
You could change your PHP to check on client_id instead (If you do this you can remove your submit button completely) :
if(isset($_POST['client_id'])){
$clientid = mysqli_real_escape_string($mysqli, $_POST['client_id']);
//MYSQL query here
}
Or change your submit button to a hidden field :
<form id="my-form" action='a.php'>
<SELECT onchange="myFunction()" name="client_id" ID="mySelect">
<OPTION value="artes>'">artes</OPTION>
<OPTION value="ingles">inglés</OPTION>
</SELECT>
<input type="hidden" name="chooseclient" value="Select">
</form>
Ajax
Just like in the first method we will add a id to your form and an onchange event to your select you should also remove your submit button or change it for an hidden field, in this example I will remove it :
<form id="my-form" action='a.php'>
<SELECT onchange="myFunction()" name="client_id" ID="mySelect">
<OPTION value="artes>'">artes</OPTION>
<OPTION value="ingles">inglés</OPTION>
</SELECT>
</form>
And the script wich will be quite different to the first one :
<script>
function myFunction(){
var form = document.getElementById("my-form");
var action = form.getAttribute("action");
var data = new FormData(form);
var xhr = new XMLHttpRequest();
xhr.open("POST", action);
xhr.send(data);
}
</script>
Again you will have to fix your PHP not to condition on chooseclient (Unless you made it an hidden field) :
if(isset($_POST['client_id'])){
$clientid = mysqli_real_escape_string($mysqli, $_POST['client_id']);
//MYSQL query here
}
If you choose the ajax method you may want to do something with the response, there are plenty of threads on stackoverflow about this, here is one : How to get the response of XMLHttpRequest?
