Source: The Great Interpretation of Dreams (Ibn Sirin)
A palm tree in a dream indicates a scholarly man or a noble Arab man, or it indicates a righteous wife, a blessed child, or long life. Cutting it indicates death or travel.
Source: Perfuming Humanity in the Expression of Dreams (Al-Nabulsi)
A palm tree indicates good words and good deeds. Climbing it indicates attaining exaltation. Its fruit (dates) is lawful sustenance.
Source: Signs in the Science of Expressions (Ibn Shaheen)
A palm tree is interpreted as a generous man or a righteous woman. Whoever sees himself planting one will be blessed with a righteous child.