I am not sure what your question really is. You are modifying @current_columns but you are keeping $current_line unmodified and store it in $previous_line for further processing. Do you want your modifications reflected in $previous_line in the next iteration of your loop? If that is the question, you should really store the array @current_columns instead of $current_line, e.g.

my $previous_line = <IN>;
chomp $previous_line;
my @previous_columns = split(" ", $previous_line);

while (my $current_line = <IN>) {
    chomp $current_line;
    my $end_coor = $previous_columns[2] + $previous_columns[3];
    my @current_columns = split(" ", $current_line);
    my $seq_length = length $previous_columns[6];
    my $gap_count = $previous_columns[6] =~ tr/Q//;
    my $original_length = $seq_length - $gap_count;
    my $original_end_coor = $previous_columns[2] + $original_length;
    my $distance = $current_columns[2] - $original_end_coor;
    $current_columns[2] = $end_coor + $distance;
    print OUT "$current_columns[2]\n";
    @previous_columns = @current_columns;
}
[download]

Not tested...