If Publishing Feature is not activated, we have only one option with the help of JQuery to perform audience targeting in Quick launch bar.
function TopSummaryBoxCalc()
{
var urls = "https://tenant/sitecollection/site/_api/web/currentUser/groups?$select=title";
var output = getListItem(urls);
}
function getListItem(urlform)
{
var a=[];
$.ajax({
url: urlform,
method: "GET",
headers: {
"Accept": "application/json; odata=verbose"
},
success: function (data) {
var dataResults = data.d.results;
for(var i = 0;i<dataResults.length;i++){
a[i]=dataResults[i].Title.trim();
}console.log(a);
var answer=$.inArray( "GROUP NAME", a );
if(answer ==-1)
{
$(".ms-core-listMenu-item:contains('node name1')").hide();
$(".ms-core-listMenu-item:contains('node name2')").hide();
}
},
error: function(xhr, textStatus, errorThrown) {
alert("error:"+JSON.stringify(xhr));
}
});
}