Try this
<?php
if ($_SERVER['REQUEST_METHOD'] == 'POST') {     
    if (!empty($_POST['LicenceNo']) && $_SESSION['MEMID'] == '')  {
        require ('sql_get_MNZID.php');                       
    }else { 
        if(isset($_SESSION['Password']) && isset($_POST['Password'])){                
            if ($_SESSION['Password'] == $_POST['Password']){
                echo '<a href="index_login.php">New Page</a>';    
            }  
        }
    }
}else{
    $_SESSION['MEMID'] = '';
    $_SESSION['Password'] = '';   
    $_SESSION['MemName'] = '';
}    
?>
**Modification:-**To redirect to another page then 
replace this
if ($_SESSION['Password'] == $_POST['Password']){
          echo '<a href="index_login.php">New Page</a>';    
} 
with this
if ($_SESSION['Password'] == $_POST['Password']){
        echo '<script type="text/javascript">location.href = "index_login.php";</script>';  
} 
It will work for you.
This works
if ($_SESSION['Password'] == $_POST['Password']){
    header("Location: mem_page.php");      
    exit;                        
}