You do not "overcome" a validator, they always run when you tell them to (i.e. put them on a transition).
You will need to change your validator so that it makes the checks you want to do. In this case, you need a validator script that says "check groups and user id of current user and if they do not match what we want, then check that a field has been filled" (instead of just "check field is filled")
https://library.adaptavist.com/entity/validate-the-user-group-of-the-assignee is an example of working with user groups.
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