The given sentence is in passive voice. In "No one has seen the new servant since last night" , The subject is "no one" and is acting upon the object 'new servant'.
When we change the sentence into passive, the Subject is being acted upon, so in passive voice, it becomes : The new servant has not been seen by anyone since last night. "no one" is changed by 'anyone' and it becomes the subject which is being acted upon.