Complex sentence: Despite this, Hank continues his investigation as best as he can (no longer LAPD, he has less access to crime info), giving a description of a tattoo he saw on the killer's wrist, but turns up dry.
Split into simpler sentences: Despite this, Hank continues his investigation as best as he can, but because he is no longer part of the force, he has less access to crime info. He looks for a description of a tattoo he saw on the killer's wrist, but turns up dry.