Get integer value of the current year in Java

This simplest (using Calendar, sorry) is:

 int year = Calendar.getInstance().get(Calendar.YEAR);

There is also the new Date and Time API JSR, as well as Joda Time

You can also use 2 methods from java.time.YearMonth( Since Java 8 ):

import java.time.YearMonth;
...
int year = YearMonth.now().getYear();
int month = YearMonth.now().getMonthValue();

int year = Calendar.getInstance().get(Calendar.YEAR);

Not sure if this meets with the criteria of not setting up a new Calendar? (Why the opposition to doing so?)

Using Java 8's time API (assuming you are happy to get the year in your system's default time zone), you could use the Year::now method:

int year = Year.now().getValue();