The simplest thing to do is to have a variable and store the information if the first pattern has been found. Like this:

my $first_pattern = 'DESCRIPTION:***Private-from-iPhone***';
my $found         = 0;
while (<>) {
    chomp;
    $found = 1 if m/\Q$first_pattern/;
    if ($found && m/SUMMARY:/) {
        ...
    }
}
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That works, with one caveat - the variable $found will not be reset when the while (<>) { ... } jumps from one file to the next.

You can fix that with a neat trick described in the eof documentation:

...
while (<>) {
   $found = 0 if eof;
   ...
}
...
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