An Administrator has a user who needs to be able to suspend and resume a...

The user needs the OPERATE privilege on the task to suspend and resume it, and the USAGE privilege on the database and schema containing the task to access it1. The EXECUTE TASK privilege is not required for suspending and resuming a task, only for triggering a new run1. The OWNERSHIP privilege on the task or the database and schema would allow the user to modify or drop the task, which is not desired.