I assume your ordered teachers are in an array @preferred, and your unsorted teachers are in @unsorted Then,

my %order = do {my $i = 0; map {$_ => $i++} @preferred};
my @sorted;
$sorted[$order{$_}] = $_ for @unsorted;
@sorted = grep {defined} @sorted;
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No sort() needed. Expected runtime: O(N), where N is the total number of teachers.