Coarsely chop the turkey and place in a medium bowl. Stir in the mayonnaise, mustard, and vinegar until combined. Season to taste with pepper.
Arrange arugula and carrot in the center of the tortilla. Spoon turkey salad down the center. Fold one end of tortilla up over a little of the filling. Fold the sides over to enclose the filling, and then roll up to close. Cut sandwich in half crosswise, wrap each half separately in waxed paper, and refrigerate overnight.