HIV-1 Reverse Transcriptase (RT) is a multifunctional enzyme responsible for the transcription of the RNA genome of the HIV virus into DNA suitable for incorporation within the DNA of human host cells. Its crucial role in the viral life cycle has made it one of the major targets for antiretroviral drug therapy. The Non-Nucleoside RT Inhibitor (NNRTI) class of drugs binds allosterically to the enzyme, affecting many aspects of its activity. We use both coarse grained network models and atomistic molecular dynamics to explore the changes in protein dynamics induced by NNRTI binding. We identify changes in the flexibility and conformation of residue Glu396 in the RNaseH primer grip which could provide an explanation for the acceleration in RNaseH cleavage rate observed experimentally in NNRTI bound HIV-1 RT. We further suggest a plausible path for conformational and dynamic changes to be communicated from the vicinity of the NNRTI binding pocket to the RNaseH at the other end of the enzyme.