Is it correct to extend a bean class and write a class which holds logic to populate the bean we extend?
I would declare variables on separate lines.


private long liveCount, daemonCount;



From Code Complete, 2nd Edition, p761:


  Use only one data declaration per line
  
  [...] 
  
  It’s easier to modify declarations because each declaration is self-contained.
  
  [...]
  
  It’s easier to find specific variables because you can scan a single
  column rather than reading each line. It’s easier to find and fix
  syntax errors because the line number the compiler gives you has 
  only one declaration on it.

The code has a temporal coupling here:


public void run() throws Exception{
    extractMetrics();
    recordToBean();
}



A maintainer easily can change the order of the called methods which brokes it. See: Clean Code by Robert C. Martin, G31: Hidden Temporal Couplings, p302
For this:


// Here to avoid code redundancy I feel it's correct to extend 
// the  ThreadMetricsBean class
// Am I wrong ?? 



It's hard to say that which would be better without knowledge about clients and typical/possible usages of these classes. You might be able to remove redundancy in the following way too:

class ThreadMetricsExtractor {
    private final ThreadMetricsBean bean = new ThreadMetricsBean();

    public void run() throws Exception {
        storeMetrics();
    }

    private void storeMetrics() {
        final ThreadMXBean threadMXBean = ManagementFactory.getThreadMXBean();
        final int liveCount = threadMXBean.getThreadCount();
        final int daemonCount = threadMXBean.getDaemonThreadCount();
        bean.record(liveCount, daemonCount);
    }
}


I've found that composition usually leads better design, cleaner and testable code than inheritance. A reference:  Effective Java, Second Edition, Item 16: Favor composition over inheritance.
The throws Exception is unnecessary here, as far I see nothing throws any checked exception inside the run method:


public void run() throws Exception{
    extractMetrics();
    recordToBean();
}


You could use integers here:


this.liveCount = threadMXBean.getThreadCount();
this.daemonCount = threadMXBean.getDaemonThreadCount();



Both called methods returns int, so liveCount and daemonCount could be ints too.