The passions described on the face of the statue survive the hands that made it.
Is this sentence correct or we have to say "is described"? If it is correct, why did we not put "is described" to make it in passive voice?
It reads well the way it is. This is short for
The passions that are described on the face of the statue survive the hands that made it.
which is the explicit passive voice version.
They both sound natural, but omitting the "that are" makes it less wordy, and so would be used by a skilled writer.
BTW, the use of "described" here is a bit unusual as it normally refers to something written in words. More likely you would hear "depicted," which is the synonym used with visual art forms.
My aside introduces another example: I could have written this last sentence as either
...which is the synonym that is used with visual art forms.
but that's too wordy for my taste, so I wrote
...which is the synonym used with visual art forms.