#!/usr/bin/perl
use strict;
use warnings;

open my $new, '<', \<<EOF;
Connection Culv=This is Line3 - New text here 
     333 333 This should be new too 
Conn Culvert Barrel=Culvert3
*
Connection Culv=This is Line1 - New text here 
     111 111 This should be new too 
Conn Culvert Barrel=Culvert1
*
Connection Culv=This is Line2 - New text here 
     222 222 This should be new too 
Conn Culvert Barrel=Culvert2
*
EOF

$/ = "*\n";
print map {$_->[0]}
      sort {$a->[1] <=> $b->[1]}
      map {[$_, /^Conn Culvert Barrel=Culvert(\d+)$/m]} <$new>;

##</code><code>##

Connection Culv=This is Line1 - New text here
     111 111 This should be new too
Conn Culvert Barrel=Culvert1
*
Connection Culv=This is Line2 - New text here
     222 222 This should be new too
Conn Culvert Barrel=Culvert2
*
Connection Culv=This is Line3 - New text here
     333 333 This should be new too
Conn Culvert Barrel=Culvert3
*