my @unsorted_input;

while (my $line = <Input>) {
    if ($line =~ /\A\[/) {      # line starts with a bracket
        if (@unsorted_input) {  # if array has entries
            >>>call your sort routine here<<<
            print @unsorted_input;
            undef @unsorted_input;
        }
        print $line;            # print the header line
    } else {                    # line is an entry line
        push @unsorted_input, $line;
    }
}
>> your sort routine <<         # added code per soonix's correction
print @unsorted_input;