First of all, everything you're assigning to @test needs to be quoted, whether explicitly or with a qw() construct.

Second, your real problem is that you're using symbolic references. $var isn't an array reference. Dominus has written the quintessential explanation of what you're actually doing, and why it's a bad idea.

The fix is to say:

my @test = qw( test trial good );
my $var = \@test;
push @{$var}, "Testing";
print join(' - ', @test), "\n";
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Relevant documentation is in perlref and perlreftut.