If chewing up the input list (or a copy of it) is acceptable, here is a solution:

#!/usr/bin/perl

use strict;
use warnings;

my @List = (1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1);
my $Tag = 5;

my @Result = ();

while (@List) { push @Result, splice @List, 0, 3 if shift @List == $Ta
+g }

use Data::Dumper;
print Data::Dumper->new([\@Result], [qw[Result]])->Indent(0)->Dump,"\n
+";

__END__
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Line 11 is the important part. As long as items remain in @List the loop iterates, shifting one item off the left edge of @List and checking if it is the $Tag value (5 in this example). If so, the next three elements are removed from @List and added to the @Result array.