First, please make sure posted code compiles. Ignoring your pseudocode, you are missing a sigil on line 16 and a comma on line 22 and a curly bracket on line 31. See How do I post a question effectively?.

If a defined condition is sufficient (rather than exists), then you can easily perform the check with a grep and Slices:

if(grep defined, @line{@{$new{a}}}) #need this condition
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Otherwise, it's probably easiest to loop over the array ref:

my $seen = 0;
for my $val (  @{$new{a}} ) {
    $seen++ if exists $line{$val};
}
if($seen) {#need this condition
    do something
} else {
    do something
}
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