See Sub array in Array of array and Eliminate Array of array duplication, and the replies and solutions you got there.

This is not a code writing service. You need to show some effort and also put effort into your problem statement. You should explain what parts of your "example" are the example, and why elements should be excluded from the result.

my @new = @array[1, 3];
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Or do you have some other criteria than index to determine which array elements should be in the new array?

It helps if you actually describe how the code should decide, and what you have tried so far. See How (Not) To Ask a Question.

my @array = ('1,2,3','1,2,3,4,5','11,12,13','11,12,13,14,15,16');

@array = do {
    my $last = '';
    reverse grep {
        $last = $_ unless 0 == index $last, $_;
        $last eq $_
    } sort { $b cmp $a } @array;
};
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