Nelson - EPSG:5766

WKT

VERTCS["Nelson", 
	VDATUM["Nelson"], 
	PARAMETER["Vertical_Shift", 0.0], 
	PARAMETER["Direction", 1.0], 
	UNIT["Meter", 1.0]]

WKT2

VERTCRS["Nelson", 
	VDATUM["Nelson"], 
	CS[vertical, 1], 
	AXIS["Gravity-related height (H)", up, 
		LENGTHUNIT["Meter", 1.0]], 
	ID["EPSG", "5766"]]

Data from @esri/proj-codes

{
  "wkid": 5766,
  "latestWkid": 5766,
  "macro": "PE_VCS_NELSON",
  "name": "Nelson",
  "wkt": "VERTCS[\"Nelson\",VDATUM[\"Nelson\"],PARAMETER[\"Vertical_Shift\",0.0],PARAMETER[\"Direction\",1.0],UNIT[\"Meter\",1.0]]",
  "wkt2": "VERTCRS[\"Nelson\",VDATUM[\"Nelson\"],CS[vertical,1],AXIS[\"Gravity-related height (H)\",up,LENGTHUNIT[\"Meter\",1.0]],ID[\"EPSG\",\"5766\"]]",
  "description": "Nelson",
  "authority": "EPSG",
  "version": "6.15(9.3.0.0)",
  "deprecated": "no",
  "areaname": "New Zealand - South Island - Nelson vcrs",
  "extent": {
    "slat": -42.44,
    "nlat": -40.44,
    "llon": 171.82,
    "rlon": 174.46
  }
}