Phoenix loureiroi ?

I had no access to reach that plant for more views.

I will let it remain labelled as-is until validated otherwise. I suggested this ID based on eliminating other 3 species of Phoenix listed in an informal checklist of Tamil Nadu Flora.

Phoenix canariensis – found in India as an ornamental plant in high-end resorts, parks, or large private estates.
Phoenix pusilla – typically a lowland/coastal species
Phoenix rupicola – its natural wild habitat is far to the north, specifically the Himalayan foothills of West Bengal, Sikkim, Bhutan, and Arunachal Pradesh. May be found in the Nilgiris, if it were planted in a garden, resort, or forest lodge.