athanasia,
You use the string concatenate operator . - see perlop.

To take this further, your grep should probably be a map. You likely shouldn't be using &fun(@arg) unless you know what the & is doing. Also, for anything more complex - you probably should use a block:

for my $thing (grep defined, @oldlist) {
    if (/(\d+-PVC_\d+)/) {
        my $item = $1;
        my $str1 = foo($item) || '';
        my $str2 = bar($item) || '';
        push @newlist, $str1 . '/' . $str2;
    }
    else {
        warn "Do not know what '$thing' is\n";
    }
}
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