This JavaScript will do the job for you - you need to supply the Team Area id, and the name of the role as text. If you wanted to use the name of the Team Area instead you could modify the script accordingly.

Note that this script will run asynchronously so that it doesn't affect the performance of your browser, which means that the results may not be available directly in your calling function

dojo.require("jazz.client");

  var jazzClient = jazz.client;

  var getTeamMembersWithRole = function(team, role) {
    if (!team || !role) {
      console.log('getTeamMembersWithRole: Error! team = ' + team + ', role = '
          + role);
      return null;
    }

    var xhrArgs = {
      url : '/ccm/rpt/repository/foundation?fields=foundation/teamArea[itemId='
          + team
          + ']/roleAssignments/(contributor/itemId|contributorRoles/name)',
      headers : {
        'Accept' : 'application/xml'
      },
      handleAs : 'xml'
    };

    return jazzClient.xhrGet(xhrArgs).then(
        function(data) {
          var memberIds = data.evaluate(
              'foundation/teamArea/roleAssignments[contributorRoles/name/text()="'
                  + role + '"]/contributor/itemId', data, null,
              XPathResult.ANY_TYPE, null);

          var members = [];
          var id = memberIds.iterateNext();

          while (id !== null) {
            members.push(id.textContent);
            id = memberIds.iterateNext();
          }

          return members;
        });
  };