Is there an easy way to do this?
Yes.
do I really have to add an additional JS file to complete this task?
No. However, time handling in JS is difficult, since it has no really cross-browser-safe date/timestring parsing and formatting methods. It can be helpful to use a library for that, however that won't be necessary for your clock.
// all three clocks represent current time
var clock1 = new Date(); // current moment
var clock2 = new Date();
var clock3 = new Date();
// for outputting, adjust them
// leave clock1 in UTC
clock2.setHours(clock2.getHours() + 3); // UTC+3
clock3.setHours(clock3.getHours() - 5); // UTC-5
// now for display, use these values:
clock1.getUTCHours();
clock1.getUTCMinutes();
clock1.getUTCSeconds();
clock2.getUTCHours();
clock2.getUTCMinutes();
clock2.getUTCSeconds();
clock3.getUTCHours();
clock3.getUTCMinutes();
clock3.getUTCSeconds();