My vector data is based on EGM2008 and I want to add local geoid to arcgis and project vector data from EGM2008 to local geoid.
If it is not possible to add custom local geoid in arcgis, how can I project/ transform 3d vector data to local geoid?
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Right now, there isn't a custom vertical transformation tool which would let the software know how to handle the local geoid file.
If the geoid file is in either US National Geodetic Survey's geoid file format or the US NGA GEOTRANS geoid file format. You would also need to use ArcGIS Pro, probably version 2.1 or 2.2. If both of those are true, there is a method that might work.
It's possible to set a system or user environment variable and some text file to define a custom transformation or coordinate reference systems. It's a bit too complicated to include here but email me (mkennedy at esri dot com) and I can send you some documentation.
Disclosure: I work for Esri.