Yes. Specifically it is possible to reload a module. The trick is to update %INC so that a subsequent call to require reloads the module. Consider:

# reload.pl
use strict;
use warnings;

for (1 .. 2) {
    delete $INC{'ReloadModule.pm'};
    require ReloadModule;

    for (1 .. 3) {
        print ReloadModule::nextCount(), " ";
    }

    print "\n";
}

# ReloadModule.pm

use strict;
use warnings;
no warnings 'redefine';

package ReloadModule;

my $count = 0;

sub nextCount {
    return ++$count;
}

1;
[download]

Prints:

1 2 3 
1 2 3
[download]

Note the use of no warnings 'redefine'; in the module to be reloaded to suppress "Subroutine nextCount redefined at ..." warnings.