It's a nice gift and a decorative piece to enjoy but not very old, I'm afraid. Stylistically, it's a bit of mishmash, with various elements that seem to be saying Han dynasty (2,000 years ago). It's been artificially aged, and the carver has tried to give a false appearance of age by making his work appear crude (the incised comma shape at 3 o'clock, for instance).

The circular disc in Chinese is called a bi (pronounced bee), and it has been an important form from the earliest times. I'll attach a couple of photos of a dark green jade bi that comes from the Dawenkou culture in NE China about 5,000 years ago. The surface has been altered in places to a brown hue as a result of the iron content in the soil in which it was buried. It's amazing how finely polished the unaltered parts of the surface still are; it must have taken months of work. But in the second image you can see irregularities in the shaping and the thickness as a result of the very simple tools available at that time.

Best,

Will