I hesitated to reply because I knew other monks would come up with a solution faster than I. I only would like to add grep for the possibility that the first array (@a1) contain non-keys as well.

Niggle :-)

This doesn't check for non-keys. It checks that each key has a defined value. In the process it auto-vivifies each key in @a1, which is probably not what you want even if you are searching for keys with defined values. For example, after running your example %h1 will be:

(
    'key2' => 'bar',
    'key1' => 'foo',
    'not_a_key' => undef,
)
[download]

Also, what if you want a key with an undef value?

If @a1 might contain non-keys they something like this will do the job.

@a2 = @h1{grep exists $h1{$_}, @a1};
[download]