Open a form from the main one and modify a principal variable without creating it again

To pass variables between forms you can use 2 paths, the first, pass it by reference:

In the target form, create a public method like this:

int ClaveActual = 0;

public void MostrarFormulario(ref int clave)
{
  this.ClaveActual = clave;
  this.txtClave.Text = clave.ToString();
  this.ShowDialog();
  this.ClaveActual = int.parse(this.txtClave.Text);
}

and on the change button, enter the following code.

public void CerrarFormulario()
{
  this.Close();
}

or else to return a value, ignore the ref and stir a value:

public int MostrarFormulario(int clave)
{
  this.ClaveActual = clave;
  this.txtClave.Text = clave.ToString();
  this.ShowDialog();
  return int.parse(this.txtClave.Text);
}

and the way you call the form would be something like this:

ChangeWin objFormulario = new ChangeWin();
//Por referencia;
objFormulario.MostrarFormulario(ref Clave);
//Por valor:
int NuevaClave = objFormulario.MostrarFormulario(Clave);

EDIT: I do not think it's even necessary to use events:

In your secondary form you add a property and its corresponding field:

private int newKey;
public int NewKey { return newKey;}

Then, where you have the code of the accept button:

private void BotonOk_Click(object sender, EventArgs e)
{
    newKey = // obtienes la nueva key
    DialogResult = DialogResult.OK;
    Close();
}

Finally, when you send a call to the secondary form:

var win = new Change_Key();
if (win.ShowDialog() == DialogResult.OK)
{
     var nuevaKey = win.NewKey();
     // aquí ya puedes actualizar la "key" de formulario
}

If you want the change to occur in real time before closing the second form you can use events.

You create an event like this:

public class KeyChangedEventArgs : EventArgs
{
    public KeyChangedEventArgs(int keyValue)
    {
        KeyValue = keyValue;
    }

    public int KeyValue { get;}
}

In your secondary form you add the event like this:

public class Change_Key: Form
{
    public event EventHandler<KeyChangedEventArgs> KeyChanged;

And where you change the value in that same form you send the event invoking:

var nuevaKey = // obtienes la nueva key desde donde se ha modificado
KeyChanged?.Invoke(this, new KeyChangedEventArgs(nuevaKey));

And nothing else remains to be hooked to the event from the main form:

var win = new Change_Key();
win.KeyChanged += (s , e) => {
    var nuevaKey = e.KeyValue;
    // aquí ya puedes actualizar la "key" de formulario principal a como la ocupes.
};
win.ShowDialog();