Have you verified your eligibility for a HK permanent identity card? If you are Non-Chinese citizen, then, you should have resided in HK for not less than 7 years, and provide your HK birth certificate. Or you was permanent resident of HK before 1997, provide your identity documents, such as proof of 7 years continuous ordinary residence in Hong Kong and proof of permanent resident status by descent. And also you are required to make a declaration that you have taken Hong Kong as your place of permanent residence.
You can submit application form, duly completed and signed together with copies of supporting documents, by post to
Right of Abode Section
Immigration Department
25/F Immigration Tower
7 Gloucester Road
Wan Chai
Hong Kong
Or, you can also use a convenient online service to submit your scanned copies of your application form and supporting documents to gov.hk. Be aware that you must be staying in Hong Kong legally when submitting applications (regardless of whether by post, drop-in or via the Internet).