startService.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View view) {
                Log.d("myE", "Start click");
                try
                {
                    Context ctx = (Context)MonitoringFragment.this.getActivity();
                    ctx.startService(new Intent(getContext(), CheckService.class));
                }
                catch (Exception e)
                    Log.d("myE", e.toString());
                Log.d("myE", "End click");
            }
}

public class CheckService extends Service
{
    @Nullable
    @Override
    public IBinder onBind(Intent intent) {
        return null;
    }

    public int onStartCommand(Intent intent, int flags, int startId) {
        try {
            Log.d("myE", "onStartCommand");
        }
        catch (Exception e) {
            Log.d("myE", e.toString());
        }
        return START_STICKY;
    }
}

<service android:name=".MonitoringFragment$CheckService" />