There is no way to 'force' a user to fill it out, but you can remind them on every page they visit until they fill it out, which I've found is very effective. Assuming that the 'type' name of your Membership Application content type is 'membership_application', you can place the following code in your template.php file in your theme folder and it will do the trick:

// Show a message if the user hasn't created their profile yet
if (module_exists('content_profile')) {
  global $user;
  // Change this type to whatever the type of your content profile is
  $type = 'membership_application';
  // Make sure the user can create the content profile first, then check if the user already has one or not
  if (arg(2) != 'edit' AND user_access('create '. $type .' content') AND !content_profile_load($type, $user->uid)) {
    // The user doesn't have one, so show a message to the user to create one
    drupal_set_message(t('You still need to fill out your profile! !link', array('!link' => l('Click Here', 'user/'. $user->uid .'/edit/'. $type))));
  }
}

If you want to really force them to fill it out, you can do the following instead of the drupal_set_message line, which will redirect them every time they visit your site to the fill out page if they haven't done so yet:

drupal_goto('user/'. $user->uid .'/edit/'. $type);

Sincerely,

Leighton Whiting