Oh, Anon, you don’t ask a fanfic writer this question!
But, no worries if you’re trolling, I will answer with my former-cheerleader level of enthusiasm!
We’ll never know how Gary Glasberg intended S11 to go. As it seemed in S12, he was teeing up to have Tony and Ziva finally admit their feelings for one another. Maybe the premiere would’ve had a similar plotline except with Ziva coming home for real. But who knows?
My answer to the question is quite simple— I wouldn’t have written her out at all. Have Tony and Ziva acknowledge their feelings, out loud and definitively, so that the fans get what they’ve been building up to for years. Instead of Tony begging Ziva to come home and Ziva basically blowing him off, I would’ve let them have a real conversation about what was happening. Maybe that would’ve been an okay way to write Ziva off the show for a bit— “Hey, Tony, I just need some time to deal with all this crap. Can I have a few months? We’ll stay in touch. Thank you for your support and I love you too. Talk soon.” (There’s many more issues I have from what I’ve heard of this arc, but I’ve never been able to stomach actually watching it so I’m not going to nitpick further.)
It would’ve been super easy to throw in a few references here and there to Tony communicating with Ziva. Tiny little touches that do not need to be explained. Maybe Tony heads back to Tel Aviv over the holidays? Maybe he references that Ziva is meeting him in NYC for the weekend? He could’ve been twitchy one episode because he sent her an email pouring his heart out and he hadn’t heard back in a day or two. He could’ve awkwardly tried to explain to a woman hitting on him that he’s “in a relationship. Well sort of. It’s long distance and not really defined…but I do love her and she would probably haul ass across the Atlantic if she thought I was even looking at another woman, which I really don’t feel the need to do anymore, I wish she would just understand that…” Maybe down the line, he contemplates a transfer overseas to be closer to her. Perhaps he just starts posting up photos and postcards she’s sent him in his cube.
Maybe one day the producers kiss and makeup with Cote and we get a fabulous episode where Tony meets up with her in Paris, presumably on a case but hey look who else is in town?
Gary Glasberg, and probably Michael Weatherly, were reluctant to tie Tony down to Ziva if Cote wasn’t going to be around. But that is just poor writing. We’ve gone SEASONS without seeing Tony in a serious relationship. No one was exactly cheering “it’s about time” when he hooked up with E.J. We’ve gone on an emotional journey with Tony DiNozzo, ten years at that point, an entire fucking decade. He’s finally worked to the point where he is ready for a Real Relationship, but that was a foundation built with Ziva in mind. Just like there were no more excuses to keep Tony and Ziva apart on the show if Cote were still part of the cast, to suddenly erase 7 years of build up now that she isn’t is disingenuous. It’s an insult to everyone who’s rooted for them for years.
Basically, the entire handling of the Tony/Ziva ship is infuriating. Forget the Moonlighting argument. Are there any TV characters currently engaged in as long of a UST relationship? (One that has an actual canon chance of being resolved?) Bones and Castle have gone down that road. Parks & Rec has done an exemplar job balancing Leslie and Ben’s relationship with the ensemble cast— highlighting both their relationship milestones and individual character growth. If we look to shows that had a lead written off and still did a fairly decent (given the less than ideal circumstances) job handling it, look at the Doug/Carol arc on ER or Mulder/Scully on The X-Files. Neither show was the same without their power couple together on screen, but at least their relationships survived and satisfied fans in the long run.
So that’s a long answer to a basic question. The answer as to how to make it believable? Stay true to the characters that have been written for the past ten years. Don’t attempt to erase and resolve a seven season long plotline in one episode, never to be mentioned again. Deal with the actress leaving the show, but don’t pretend the character never existed, especially when the driving theme of her character was her search for home and family.