No, airbnb will not do anything about this- hosts and guests are welcome to review or not.
If the guest was a good one and the 14 day review period is almost up, you could always message them on the airbnb messaging system and say how pleased you were to host them and that since you are a fairly new host, you'd really appreciate them writing a short review so other guests will have more reviews to see.
Did you write the guest a review? When you do, the guest will be prompted on their email by airbnb to write one. that said, some guests just can't be bothered.