65Stang,
There are some restrictions about removing trees, and I am note sure if it covers large healthy palms. I would suggest calling ARC, here is the link,
VCDD Architectural Review and the phone number
Community Standards Phone: 352-751-3912.
Better safe then sorry, there can be a significant fine if a tree is removed without permission.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV.