As it’s portrayed on the map up north close to the northern terminus (at I-84), this route is east of the Taconic State Parkway’s two exits off I-84.
Westchester County Airport (HPN), services - among other airlines - just American and Delta airlines, and a wealth of private flights for private services - via MillionAir - yet its main terminal only has one door to check-in.
In fact, the Wikipedia page pulled up on November 28, 2021, even revealed that Connecticut’s Department of Transportation pays New York State’s Department of Transportation for New York to plow and maintain the interstate over the Connection section of the highway. [3] X Research source because Connecticut doesn’t have rights to travel New York’s streets and due to no exit being there gives trouble. Biggest things you might spot on the route through Connecticut include the Tamarack Country Club - if it wasn’t for the fact that there are many trees in the way.
NY-22 is also accessible from NY-172 east - just in case you passed the last exit and need to head on NY-22.
The Wikipedia page mentions it travels to NY-117 and New York City, but that’s referencing routes at the southern terminus of the parkway.
According to Google Maps for PC (website), you’ll notice how it’s accessible only from NY-22 from the northbound strip of highway, yet the cross-street enters the highway from NY-138. You might not notice the station right from the exit if you’ve taken the exit traveling northbound. Exit off the highway and head to NY-22. Take that north and as it travels parallel to the highway, you’ll encounter the cross-street NY-138 and the one nearest the railroad station.
Again, northbound exits with southbound entrances onto the highway.