mysql> SELECT p.id, p.project_name, p.client_id, c.client_name FROM project p LEFT JOIN client c ON p.client_id = c.id WHERE p.active_flag = '1' ORDER BY c.id DESC ;

+-----+--------------------------------------------------------------+-----------+-------------+
| id  | project_name                                                 | client_id | client_name |
+-----+--------------------------------------------------------------+-----------+-------------+
|  50 | Aリスト                                           　　　　　　　　|         9 | admin       |
| 188 | Bリスト                                                        |         9 | admin       |
|   7 | Cリスト                                                        |         2 | user      |
|   8 | Dリスト                                                        |         2 | user      |

//データベースへ接続する。
$dsn = 'mysql:dbname=yourdbname;host=yourhost';
$user = 'youruser';
$password = 'yourpass';
$dbh = new PDO($dsn, $user, $password);

// SQL文を実行する。
$sql = "SELECT p.id, p.project_name, p.client_id, c.client_name
        FROM project p LEFT JOIN client c ON p.client_id = c.id
        WHERE p.active_flag = '1'
        ORDER BY c.id DESC";
$sth = $dbh->prepare($sql);
$sth->execute();

//SQL文で指定したすべてのデータを取得する。
$result = $sth->fetchAll();

//データをclient_id,project_idごとに配列へ格納する。
$data = array();
foreach($result as $project){
    $client_name = $project['client_name'];
    $project_id = $project['id'];
    $data[$client_name][$project_id] = $project;
}

print "<ul>";
foreach($data as $client_name => $projects){
    print "<li>{$client_name}";
    print "<ul>";
    foreach($projects as $project){
        print "<li>{$project['project_name']}</li>";
    }
    print "</ul>";
}
print "</ul>";