Trying to explain
The anterior cleft palate is associated with cleft lip and definitely it does not involve the nasal septum.
They usually call it Primary Cleft Palate (not anterior).
The Primary Cleft Palate is caused by failure of fusion of the Medial Nasal Prominence (later on called Intermaxillary segment or Primary Palate or Philtrum or later on soft palate) with the Maxillary Prominence.