Foreign nationals are allowed to cross the Russian border only on a valid national passport and a valid Russian visa therein.
If you get a new passport you are required to transfer the valid Russian visa in an invalid passport to the new one or apply for a new visa. Visas in lost/damaged passport must also be transferred to the new passport before you travel.
A foreign national will be denied entry to the Russian Federation with a valid Russian visa stamped in an invalid (cancelled, expired, etc.) national passport.