While Roger gave you some solutions, I wonder if you really need a new hash, or if you just need to use the values once.

You could get the values like this:

my %hash = ( "NETWORK1" => "A", 
             "NETWORK2" => "B", 
             "TYPE1"    => "C", 
             "TYPE2"    => "D");
             
my @networks = @hash{ grep /^NETWORK/, sort keys %hash };
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You could even pass the values into a function directly, instead of catching them in the array first. It just depends on what your goal is.