Ghost Kate was a spiritual manifestation or rather a ghost image of deceased NCIS Special Agent Caitlin Todd who died after being shot in the head by Ari Haswari in the last few seconds of the Season 2 finale episode, Twilight (episode).
Biography
NCIS Season 3
In "Kill Ari Part 1", Ghost Kate first appeared in the NCIS Season 3 premiere episode, "Kill Ari Part 1" where she confronted NCIS Special Agent Leroy Jethro Gibbs over his failure to stop her impending death from happening when it had been clear to the entire team that Gibbs was the one Ari had wanted to kill, not Kate.
She even asked Gibbs why she had been the one to die, only for Gibbs to tell her that he didn't know before yelling at him why she had died instead of him but the ghost disappeared when NCIS Special Agents Anthony DiNozzo and Timothy McGee arrived into the Bullpen.
Kate later appeared to Abigail Sciuto in Abby's lab dressed as a Goth and the two then discussed the fun times they'd had together. Kate's ghost even revealed that she liked seeing Abby wearing pigtails and having black lipstick which Abby did just before she got to work.
In Autopsy, Ducky spoke to Kate who told him about what happened during the hostage situation and about her unwillingness to kill Ari at the time which Kate stated had been caused by her looking into Ari's eyes and seeing something there that had made Kate not want to kill Ari although Ducky remarked that Ari's eyes were like ice to him.
Later, DiNozzo even imagined Kate dressed in a Catholic schoolgirl uniform much to her horror.
McGee also had two visions of Kate, the first one of her wearing a cat-suit similar to that of Trinity from the Matrix movie series while the second had Kate in a black-leather BDSM styled outfit complete with a whip which had McGee remarking to his own dismay that he was becoming more like Tony.
She later reappeared to Gibbs in "Kill Ari Part 2" as he searched for Donald Mallard and Gerald Jackson, both of whom Gibbs suspected Ari had kidnapped and in a malicious tone, suggested that Gibbs kill himself to save the entire team as a means of making things right again.
She even appeared to McGee who was busy working on the case, asking him why he hadn't come down to see her and that if he didn't look at the back of her head, then it would just look like she was asleep when she was actually dead. She also told him that she was so lonely she'd even welcome a visit from Tony.
After Ari died at the hands of his control officer and half-sister, Gibbs attended Kate's funeral where he saw a final vision of her telling him that he was late for her funeral and unlike the other visions Gibbs had witnessed, this Kate was peaceful, suggesting she had finally accepted her own death.
It was also shown that she had been awarded the Presidential Medal of Freedom, presumably due to her work as an NCIS Special Agent and in protecting Gibbs from Ari.
NCIS Season 12
Personality
Presumably having been created from the subconscious of Gibbs, McGee, Abby, Ducky and Tony, Ghost Kate wielded about five different personalities.
When she first appeared as a fragment of Gibbs's subconscious with Gibbs also harboring guilt over her death, Ghost Kate was aggressive and angry as well as cold to Gibbs with Ghost Kate demanding to know why she'd taken two bullets for himself before yelling why had she died instead of Gibbs.
She later returned once again and also voiced her thoughts about Ducky who Ari had taken hostage before even grimly suggesting that Gibbs should kill himself to stop Ari from hurting Gibbs's colleagues.
While in Abby's lab, Ghost Kate was charming and upbeat, telling Abby to cheer up and that she loved Abby wearing pigtails. She even displayed some embarrassment over the fact that she had a tattoo that Ducky was going to see while performing an autopsy on her.
In the morgue, while talking to Ducky, Ghost Kate's personality took on a serious side as she voiced her concerns and regrets at not having been able to kill Ari during the hostage situation in the morgue.
In the lab next to Ballistics, Ghost Kate first displayed a playful side to McGee, reflecting on the fact that he was becoming more and more like Tony. She later developed a seductive side much to McGee's own embarrassment.
Appearance
As a manifestation of Kate's self which appeared to Gibbs, Ghost Kate was exactly identical to Kate except for the fact that as a ghost, she had the bullet-shaped hole in her forehead.
When she appeared to Abby, Ghost Kate wore a black dress, a ring on both her left and right hands, the two rings on both her respective middle fingers.
She also had white hair, presumably a wig of some sort that hung down past her shoulders and she also wore a cross around her neck.
Later, in the morgue, to Ducky, Kate simply spoke to Ducky and lay on the slab, a single sheet covering her lower body.
In the lab area next to the Ballistics Lab, Ghost Kate first appeared to McGee, wearing a latex catsuit similar to Trinity from the Matrix movies. Her outfit later changed to resemble that of a BDSM dominatrix which saw Ghost Kate wearing a upper leather body-suit with cuffs on both her wrists, tights on her legs with a whip in her right hand, a collar around her neck and a leather hat on her head. She also wore black leather shoes.
When she reappeared to Gibbs, Ghost Kate's appearance remained exactly the same and she appeared to be untouched by the rain.
Ghost Kate's third and final appearance to McGee consisted of her lying in the office drawer with a single sheet covering her body.
Her overall final appearance came in "Kill Ari Part 2" where she wore a single grey shirt with white frilly edges with the rest of her outfit unseen as she was in the coffin. She also had the Presidential Medal of Freedom around her neck and prayer beads resting in her hands.