Is it permissible for an employee who works in a ministry, whose attendance is once a week, and who has no work because he is a field worker, to go out to perform private errands such as going to the club and returning, knowing that the manager does not object to it?

If the manager is authorized and the departure does not harm the work, then there is no objection. Otherwise, it is not permissible because the employee is a special hire, and their employer owns their benefits during working hours. The departure of the manager or anyone else does not justify negligence in work.