The invention pertains to an inducible CRISPR system for controlling expression of a CRISPR complex with an inducible fusion promoter. One embodiment of the invention provides HIV LTR-minimal Drosophila hsp70 fusion promoter that can be used for inducible co-expression of gRNA and Cas9 in HIV-infected cells to target cellular cofactors such as Cyclin T1. A single introduction of such embodiment leads to sustained suppression of HIV replication in stringent, chronically infected HeLa-CD4 cell lines as well as in T-cell lines. In another embodiment, the invention further relates to enhancement of HIV suppression by incorporating cis-acting ribozymes immediately upstream of the gRNA in the inducible CRISPR system construct. The inducible fusion promoter is adaptable for other tissue- or cell-type specific expression of the inducible CRISPR system.