Are you looking to apply for TSA precheck, if you mainly or only travel domestically, or are you looking to apply for GOES, which is for both international and domestic flights, and includes Precheck, for only an additional $15?
You can certainly apply at West Palm Airport, and you can find their hours and directions, here:
It is recommended that you pre-apply online, first, and make an appointment to visit the airport's TSA Enrollment Center for your interview, to save time. You can certainly walk in without an appointment, but you might have to wait longer to be seen.
Here is information about the application process:
I hope this helps.
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