The Director of Finance shall pay a Renters' Property Tax Relief Supplement to each resident who qualifies to receive a payment under the State property tax relief program for renters established pursuant to the Annotated Code of Maryland, Tax-Property Article, Section 9-102. For each taxable year, the Supplement to each eligible resident under this Section equals fifty percent (50%) of the State payment to the resident. The Director may require each eligible resident to submit an application for the Supplement, and may take any other action necessary to administer the Supplement. The County Executive may promulgate regulations to govern the implementation of this Section.