Colonel Jasper Shepard was the father of former NCIS Director Jennifer Shepard.
Colonel Shepard was a career military officer. While working in his final posting at the Pentagon, he was the subject of an investigation for allegedly taking a bribe from arms dealer, René Benoit aka "La Grenouille" and the death was believed to be a suicide.
Jenny, on the other hand thought otherwise and began to believe that Benoit aka "La Grenouille" was the origin of the allegations against her father and as such set a plan in motion that she hoped would end with La Grenouille being captured and brought to justice for his involvement in her father's death.
During the course of the investigation into the bribery allegations, Colonel Shepard was believed to have committed suicide. However, someone tried to convince Jenny that Colonel Shepard faked his suicide without her knowledge. In the Season 4 episode, Trojan Horse (episode), Colonel General Borov told Jenny that her father had visited him three weeks previously, smoking a cigar.
After her return from Europe in the Season 4 finale episode, Angel of Death (episode) she found a bottle and glass sitting on the desk in her study. Examination of the items yielded fingerprints, and the fingerprints were identified by Abigail Sciuto as belonging to Colonel Shepard.
Director Shepard attempted to delete the record of the match, but did not confirm it before she left the lab. Abby subsequently discovered the truth and informed Gibbs of what was going on.
Although, later it is hinted to that someone was gaslighting Jenny and that Jasper Shepard was actually dead. A polygraph was scheduled urgently for all NCIS agents including the director.
Tobias Fornell told Gibbs that the polygraph was by request of the CIA, targeting Director Shepard. Gibbs put two and two together and suggested that the CIA was trying to convince her that her father was alive, so that on her polygraph she would be hesitant when asked the question, and consequently fail.