Latent HIV-1 provirus represents the barrier toward a cure for infection and is dependent upon the host RNA Polymerase (Pol) II machinery for reemergence. Here, we find that inhibitors of the RNA Pol II mediator kinases CDK8/19, Senexin A and BRD6989, inhibit induction of HIV-1 expression in response to latency-reversing agents and T cell signaling agonists. These inhibitors were found to impair recruitment of RNA Pol II to the HIV-1 LTR. Furthermore, HIV-1 expression in response to several latency reversal agents was impaired upon disruption of CDK8 by shRNA or gene knockout. However, the effects of CDK8 depletion did not entirely mimic CDK8/19 kinase inhibition suggesting that the mediator kinases are not functionally redundant. Additionally, treatment of CD4+ peripheral blood mononuclear cells isolated from people living with HIV-1 and who are receiving antiretroviral therapy with Senexin A inhibited induction of viral replication in response to T cell stimulation by PMA and ionomycin. These observations indicate that the mediator kinases, CDK8 and CDK19, play a significant role for regulation of HIV-1 transcription and that small molecule inhibitors of these enzymes may contribute to therapies designed to promote deep latency involving the durable suppression of provirus expression. IMPORTANCE A cure for HIV-1 infection will require novel therapies that can force elimination of cells that contain copies of the virus genome inserted into the cell chromosome, but which is shut off, or silenced. These are known as latently-infected cells, which represent the main reason why current treatment for HIV/AIDS cannot cure the infection because the virus in these cells is unaffected by current drugs. Our results indicate that chemical inhibitors of Cdk8 also inhibit the expression of latent HIV provirus. Cdk8 is an important enzyme that regulates the expression of genes in response to signals to which cells need to respond and which is produced by a gene that is frequently mutated in cancers. Our observations indicate that Cdk8 inhibitors may be employed in novel therapies to prevent expression from latent provirus, which might eventually enable infected individuals to cease treatment with antiretroviral drugs.