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I certainly understand that you want a written agreement to have leverage against them so that there is confidentiality maintained. However, the problem is that you need leverage first to even get them to sign something like that.
Confidentiality doesn't automatically attach to very many things. Statements that may have come out during a deposition are not legally confidential unless there is a signed agreement beforehand or after that makes them confidential (which is what you want here).
However, there is no way to compel someone into confidentiality after the fact. You can't claim defamation because that requires untrue statements about you being made, and that isn't the argument here. You're claiming a violation of trust, but without a written confidentiality agreement, there is really no way to prove that it is a violation of trust, or even that they had a legal requirement to maintain that silence.
Unless you have either something to offer them or something legitimate to legally threaten them with (a lawsuit for some other matter), you have no leverage to even negotiate to obtain a confidentiality agreement from them.
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