I went through the code, making changes mostly for practice. It is *untested*. Hopefully the comments are of use. Furthermore, hopefully others can criticize me for my deficiencies:

#use strict;

# don't disable strict. Period.

# you are only using $comparetime within the compare() function
# If you define it here, then it should be passed to the sub as
# a parameter

my $comparetime="0";

# sub compare; # no need for this

my $Clinrxdir="D:\\StoreAccess\\shared\\sup shared\\";

opendir(DIR,$Clinrxdir);
my @Files= readdir(DIR);
closedir(DIR);

for my $cpupdate (@Files){

    if($cpupdate =~ m/\s*cp_/i){

        my $m_time = (stat($Clinrxdir.$cpupdate))[9];

    # what does a print() say about $m_time here?

        my ($i_wday, $i_month, $day, $year) = (localtime($m_time))[6,4
+,3,5];
    
    # why are you breaking $m_time up. Depending on what you want to d
+o,
    # it may be easiest to simply compare $m_time as an int

        my $comparison = compare($orig_mtime, $cmp_mtime $cupupdate);

        print "Timestamp for " . $cpupdate . " " . $m_time ."\n";

    }
}

# I'm lost as to where $file comes from here...

print "This is a test of file = " . $file . "\n";
print $file;

system("pause");


sub compare(){
    my ( $orig_mtime, $cmp_mtime, $cpuupdate ) = @_;
    if($cmp_mtime > $orig_mtime){
        my $file = $cpupdate;
    }
    else{
        #else{$comparetime=$string;}
    
    # it looks like you are trying to cause more than one side
    # effect with your subroutine, as opposed to focusing on providing
    # a single return. Personally, I've learned that mixing function
    # programming with global data will lead to bugs that are very
    # difficult to track down.
    
    # if you want to set $comparetime to $string, you should do it 
    # outside of this routine, after you've collected up compare()
    # result
    }
}
[download]

Steve