I believe this might be a little buggy, unless I misunderstand the requirement. But take a look at:
use strict;
my $input='
This is sample <This is sample text>
This is sample &lt;Th<a> </a>is is  sa<not a>mple text <a>this is samp
+le text</a> sample text >';

my @arr=$input=~m#&lt;[^<>]+(?:<a>.+?</a>[^<>]*)?>#g;
print join "\n",@arr;

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I'm wondering about what might be inside <a>..</a>, and whether they should be balanced. In case not, you could simply go for: 
qr {&lt;(?:[^<>]+|<a>|</a>)*>}

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Or perhaps:
qr {&lt;(?:[^<>]+|<a>|</a>)*[^>]*>}

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Otherwise, you might try:
my $re;
$re=qr{(?:[^<>]+|<a>(??{$re})?</a>)*};
my @arr=$input=~m#&lt;$re>#g;

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In reply to Re^2: encode HTML entities with a regexp by Ido
in thread encode HTML entities with a regexp by Anonymous Monk

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