can a person who has an extensive criminal records but has completed his parole requirements successfully, apply and obtain a TLC licence
Yes, it's possible to get a TLC licence after completing parole and getting a Certificate of Relief of Civil Disabilities; however, you may still be denied the licence if your prior conviction is rationally relate to to a TLC licence. For example, if you were convicted of robbery or kidnapping, then you will have a very difficult time in convincing the Board that you have been rehabilitated.