This code works like I want it to.

It does?    Really?    OK.

#!/usr/bin/perl
use strict;
use warnings;
our $list;
our @clients;
our $filedef1=$ARGV[0]; #name of client CSV file

Why are you declaring those variables here when you are only using them inside the read_clients() subroutine?

&read_clients ();

You shouldn't use & when calling subroutines, see perlsub for reasons why.

# define regex components
my $accode = qr(^"(.*)",.*,.*,.*,.*,.*,.*,.*,.*,.*,.*,.*,.*,.*,.*)x;

my $name = qr(^.*,"(.*)",.*,.*,.*,.*,.*,.*,.*,.*,.*,.*,.*,.*,.*)x;

Why include the empty fields after the captured field?

# do regex matches
print "Extractions:\n";
my @extractions = $list =~ m{(?: $name)}mxgc;

Why are you using the /c option? It is only relevant if you are using the \G zero-width assertion in the pattern.

print "$extractions[$_], " for 0.. $#extractions;
print "End of Program!\n";
##Beginning of subroutine for reading the document source file.
sub read_clients
{
open FILEDEF1, "< $filedef1" or die "error reading $filedef1-$!";
while (<>)

The special <> readline operator will treat @ARGV as a list of file names and open and read each line from all of those files. Since $filedef1 is the first element of @ARGV the file will be opened and the first line from that file will be read into the $_ variable.

    {
    push (@clients, <FILEDEF1>);

You are pushing all the lines from the file onto the @clients array from inside the loop so you should have the number of lines times the file in the array.

    }
close FILEDEF1;
$list = join(' ',@clients);

You are joining the lines together with a single space character. That may confuse the /m option on regular expressions? That means that every line except the first will have a space at the beginning.

 print $list;
} ##End of block for reading the document source file.