Try this, maybe there is an easier way, but at the moment here is what should work, hoping you are on some linux flavor, if not, then let me know what flavor of UNIX are you on, we may have to modify /bin/ksh to /usr/bin/ksh or wherever ksh is on your UNIX variant.
Put the the list of new* names in a file called /tmp/list. Put the below code in /tmp/script.sh and chmod +x /tmp/script.sh
Run the script in the directory where you have the new* files by running the script as /tmp/script.sh, when you run the script, it will echo out the moves/renames, if you like what you see, remove the echo in front of the mv, and then run it.
#!/bin/ksh
for i in `cat /tmp/list`
do
A=`echo $i|awk -F"_" '{print $2}'`
echo "mv $i old_$A"
done