In fact, you MUST operate your transponder (if you have one) in controlled airspace.
The ADSB-required rules apply to what we used to know as the places you HAD to have a transponder/encoder before.
You should absolutely continue to use your transponder since it will make you visible to appropriately equipped aircraft.
Well, very few aircraft are "appropriate equipped" to see a simple transponder. What it does is make your position and altitude known to ATC radar which then can relay it via the various traffic information services as well as making it available to controllers. Still, you want it on.