Updating JComboBox without closing and opening GUI Frame again

A person wishes to add a NEW Job to the database. A `Combobox` list the existing employers already in the database for the new Job to be added against. But if an employer is not present customers have the option click on a button to add an employer. Once added that employer should immediately be displayed in the textfield.

I am trying to achieve the above scenario with my coding and mysql database, but cant think of the logic to do so...

Table Employer

CREATE TABLE "Employer" ("employerID" INTEGER PRIMARY KEY  NOT NULL ,
    "name" CHAR,
    "industry" CHAR,
    "contact1" CHAR,
    "contact2" CHAR,
    "email" CHAR,
    "website" CHAR,
    "facts" CHAR,
    "phone" VACHAR)

Table Job

CREATE TABLE "Job" ("jobID" INTEGER PRIMARY KEY  NOT NULL ,
    "employerID" INTEGER,
    "title" CHAR,
    "description" CHAR,
    "type" CHAR,"salary" CHAR,
    "benefits" CHAR,
    "vacancies" INTEGER,
    "closing" CHAR,
    "requirement" CHAR,
    "placement" BOOL,
    "applyTo" CHAR,
    "status" CHAR,
    "posted" CHAR, 
    "location" CHAR)

Class Employer_GUI - Consist of a simple form and save button which saves new EMPLOYERS into `Employer` table

 private void SaveEmpButtonActionPerformed(java.awt.event.ActionEvent evt) {
            
        try {
            String sql = "INSERT INTO Employer (name,industry,contact1,contact2,email,website,facts,phone) VALUES (?,?,?,?,?,?,?,?)";
            pst = conn.prepareStatement(sql);
        
                        pst.setString(1, txtName.getText());
                        pst.setString(2, txtInd.getText());
                        pst.setString(3, txtC1.getText());
                        pst.setString(4, txtC2.getText());
                        pst.setString(5, txtEmail.getText());
                        pst.setString(6, txtWeb.getText());
                        pst.setString(7, txtFacts.getText());
                        pst.setString(8, txtPhone.getText());
                        pst.execute();
            JOptionPane.showMessageDialog(null, ""+txtName.getText()+" added to database!");
            this.setVisible(false);
        }
        
        catch (Exception e) {
                JOptionPane.showMessageDialog(null, ""+txtName.getText()+" could not be added!");
        }
        finally {
           try {
            rs.close(); pst.close();  }
             catch(Exception e) { } }  

    }

//Class Job_GUI - Consist of a FORM to add JOBS only to `Job` table

 private void fillCombo() {
        try {
            String sql = "SELECT * FROM Employer";
            pst = conn.prepareStatement(sql);
            rs = pst.executeQuery();
            
            while(rs.next()) {
                String empName = rs.getString("name");
                comboEmployer.addItem(empName);
                
            }
        }


How could the `JComboBox` `comboEmployer` be immediately have the selected item as the new Employer name just added?