Ecco come puoi convertire la tua query di stringa in Zend_Db_Select
class Empleaveapplication extends Zend_Db_Table_Abstract
{
protected $_name = 'tbl_empleaveapplication';
}
$table = new Empleaveapplication();
// create sub query
$subSql = $table->select()
->setIntegrityCheck(false)
->from(array('em' => 'tbl_employeemaster'), array('firstnm'))
->where('idemp = empl.approvedby', '');
// main query
$sql = $table->select()
->setIntegrityCheck(false)
->from(array('empl' => 'tbl_empleaveapplication'), array('idemp', 'approvedby' => new Zend_Db_Expr('(' . $subSql . ')')))
->joinInner(array('emp' => 'tbl_employeemaster'), 'empl.idemp = emp.idemp', array())
->joinInner(array('lvm' => 'tbl_leavemaster'), 'empl.idleavemaster = lvm.idleavemaster', array());