As of March 2018, there is a lot of confusion among stock brokers whether it is mandatory to link Aadhar to Demat / Trading account or not.
If you are opening a new Demat / Trading account, it is better to link your Aadhar at the time of opening to avoid inconvenience of compliance in the future.
If you already have a Demat Account , you may be not required to link the Aadhar immediately.
Zerodha Stock Broker has made this announcement on March 20th 2018.
The Rest of the Stock Brokers might be waiting for some clear instruction from the SEBI or Govt. regarding the same.
However, Call your Stock Broker to double check this requirement.
They way things are at the moment, there is no need to rush.