Does TRACON airspace override Class B airspace in terms of control authority when controlling approach or departure procedures? This is a simple schematic description of Class Airspace.

My understanding is that Class B has strict rules, specific lower and upper altitude limits and requires clearance to enter. However, I have also come across the Standard Operating Procedures Manual for the N90 TRACON (ORDER 7110.1D), which designate the sectors of local airspace differently. Those also define lower and upper altitude limits. Clearly, the N90 TRACON overlaps with the Class B airspace around the JFK, LGA, TEB and EWR airports.

My confusion has to do primarily with this overlap. I was thinking that Class B airspace has to do strictly with terminal procedures (approaches/departures), that is, all take-off and landing procedures take place within this airspace.

However, I have seen SID and STAR procedures running over fixes located close to the airports, which define much higher altitudes than the Class B upper limits (around JFK and the above airports, the upper limit is 7000ft for Class B airspace, while lower limits vary).

Take, for example, the LENDY SIX ARRIVAL, of JFK airport. I read over the JENNO fix information: "Expect FL230".

What is this supposed to mean: "Expect FL230"? Will an approaching aircraft enter the procedure at a Flight Level of 23000ft or be at that flight level whenever approaching the airport at that fix point? How does Class B relate to these operations? I thought that approach operations take place within Class B but I am confused because the altitudes I see in SID/STAR procedures or the lower/upper altitude limits in the various airspace sectors of Standard Operating Procedure (SOP) plans* are quite different. It appears as if flights that approach for arrival, for example, are controlled before entering Class B (i.e. at higher altitudes) when inside a TRACON, e.g. N90.

*(I cannot link to an SOP Manual because they are intended for internal distribution, so I cannot find something official online, however, the information is pretty much like that document).
Class B is a legal restriction for pilots. ATC has to give them clearance to enter it. It's there to protect the traffic around a busy airport from aircraft that are not being controlled by ATC. 

The TRACON airspace is just for controllers. Pilots aren't expected to know sector boundaries. They don't have to worry about that at all. Each controller will tell the pilot the frequency to contact the next controller whose airspace they are about to enter. Few TRACONs make their sector boundaries public and they change often.

A pilot flying under VFR does not necessarily even need to talk to controllers outside of A, B, C or D airspace, regardless of what ATC sector he might be in.

As long as you have the correct type of transponder, it is entirely legal to fly VFR through the layer of air above the class B below 18,000 feet without contacting atc. (This is class E airspace). Whatever controller whose sector you're flying through will keep any IFR traffic away from you, but they don't need to give you vectors or anything. You have to stay away from clouds. It's entirely the pilot's responsibility to see and avoid things.*

SIDs and STARs are only used by IFR traffic that is being controlled by ATC, but not necessarily by TRACON the whole time. Some STARs start hundreds of miles from the airport. When they begin the arrival they will be controlled by en-route controllers, who will tell them when they need to switch to TRACON and what frequency to use. 



* I'm leaving out flight following for simplicity.