The latent HIV reservoir is a major barrier to HIV cure. Combining latency reversal agents (LRAs) with differing mechanisms of action such as AZD5582, a non-canonical NF-kB activator, and I-BET151, a bromodomain inhibitor is appealing towards inducing HIV-1 reactivation. However, even this LRA combination needs improvement as it is inefficient at activating proviruses in cells from people living with HIV (PLWH). In this study, we performed a CRISPR screen in conjunction with AZD5582 & I-BET151 and identified a member of the Integrator complex as a target to improve this LRA combination, specifically Integrator complex subunit 12 (INTS12), as we see enrichment of this gene over all others. Integrator functions as a genome-wide attenuator of transcription that acts on elongation through its RNA cleavage and phosphatase modules. We observed knockout of INTS12 improved latency reactivation at the transcriptional level in J-lat cells compared to the safe-harbor locus AAVS1 knockout. INTS12 knockout is also more specific to the HIV-1 provirus than AZD5582 & I-BET151 treatment alone as we see less host cell gene dysregulation compared to HIV induction. When we measured INTS12 binding by CUT&Tag we observe more INTS12 at the promoter of our control cells vs our INTS12 knockout cells, therefore its effect on HIV may be direct. Additionally, by CUT&Tag, we observed more RNAPII in the gene body of HIV only with the combination of INTS12 knockout with AZD5582 & I-BET151, indicating that INTS12 induces a transcriptional elongation block to viral reactivation. Moreover, knockout of INTS12 increased HIV-1 reactivation in CD4 T cells from virally suppressed PLWH ex vivo, and we detected viral RNA in the supernatant from CD4 T cells of all three virally suppressed PLWH tested upon INTS12 knockout suggesting that INTS12 prevents full-length HIV RNA production in primary T cells. Finally, we found that INTS12 more generally limits the efficacy of a variety of LRAs with different mechanisms of action, as we see more virus with INTS12 knockout than any of the LRAs/stimuli alone.