I am trying to calculate the optical absorption of negative NV center in diamond using HSE06 hybrid functional however I am getting absorption of the defect around 2.6 eV not 1.945 eV as literature
I assume you are using TDDFT, right? It is a nice tool, but don't expect exact agreement. A shift in this order of magnitude isn't that strange, e.g. in this work on Y2O3 HSE06 also overestimates the absorbed energy by 0.36 eV:
Article Determination of the Electronic Structure and UV−Vis Absorpt...
So, these authors had the luck that HSE06 was a bit better for their system giving a smaller blueshift, but 0.655 eV is nothing to beat yourself up about.