Not out-of-box. A ServiceNow employee confirmed on a related thread that Dynamic Translation / Translate button visibility cannot be restricted by group or user through standard configuration the only native control is a system property that restricts it by table, not by user/group.
If you need per-group/user control, you'll have to build it yourself:
If the Translate button is a widget in Service Portal, clone it and add a server-side check like data.showTranslate = gs.getUser().isMemberOf('your_group_sys_id');, then wrap the button markup in <div ng-if="data.showTranslate">.
If it's rendered through UI Builder / a newer experience, you'd similarly need a custom component with a visibility condition tied to gs.getUser().isMemberOf(...) or a role check, since there's no native config field for this.
So the practical answer for the original poster: this isn't a missing setting they overlooked it's a genuine platform gap, and any group/user level restriction requires custom widget/component work.
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