Time Conversion From One Specific Timezone To Another

I would like to know how to convert a time from one specific timezone to another specific timezone. The code does not convert the time correctly. But if I replace Date

date = sdfAlien.parse("16:00:00"); to Date date = new Date();

then conversion works but that's not what I want as my input will be supplied by users with time in HH:MM:SS and Java supported timezone.

In below case, we can say "16:00:00" and "Asia/Singapore" will be supplied by the user and I need to convert it to America/New_York time.
 
SimpleDateFormat sdfAlien = new SimpleDateFormat("HH:mm:ss");SimpleDateFormat sdfLocal = new SimpleDateFormat("HH:mm:ss");sdfAlien.setTimeZone(TimeZone.getTimeZone("Asia/Singapore"));
sdfLocal.setTimeZone(TimeZone.getTimeZone("America/New_York"));
try {Date date = sdfAlien.parse("16:00:00");String alienTime = sdfAlien.format(date);
String localTime = sdfLocal.format(date);System.out.println("Local Time:" + localTime + ", Alien Time:" + alienTime);
} catch (ParseException e) {e.printStackTrace();}