Here is one way.

my $new_key   = 'NEW';
my $new_value = 'Value';

if (exists $file_hash{$new_key} &&
    $file_hash{$new_key} eq $new_value) {

    # add to another hash, per the comment in your post
}
else {
    $file_hash{$new_key} = $new_value;
}
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We are testing whether it exists or not to catch the case when $new_value is undefined and $new_key does not exist in the hash. If the $new_value == undef, then no matter what the key is (if it doesn't exist) a true value will be returned because the key in the hash HAS a value of undef.