I've clipped a polyline shapefile with polygons, which produced a new feature class with obviously less polylines. However, the attribute table for the new feature class calculates the length of the polyline from the previous attribute table, which is clearly wrong. For example, the new attribute table gives me the length of the previous polyline, even though only some of is highlighted in the new feature class. How can I find the length of only the highlighted polylines?
Open up the attribute table of the new polyline feature class. Go to the field that contains the feature length, right-click, and click "Calculate Geometry." This will honor a selection, so if you only have a few polylines selected, it will only populate the attributes of those selected features.
Also, if you were using a file geodatabase, the feature length (in a field called Shape.Length) would be populated automatically with the new values. This difference between shapefiles and geodatabases isn't, as far as I know, well-covered in ESRI's initial training materials, and the only reason I'm not telling you to just Google it.
you can read Esri's documentation here: http://desktop.arcgis.com/en/arcmap/10.3/manage-data/tables/calculating-area-length-and-other-geometric-properties.htm