my $oldhandler = $SIG{SOMETHING};
$SIG{SOMETHING} = sub {
 # do whatever 
 if ($oldhandler) {
    $oldhandler->();
 }
};
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1. this assumes that the other code does something like this as well, or that your handler is installed after the old one. See for instance my pretty simple CGI::HTMLError.

2. some kinds of signals (like SIGCHLD) are more complicated than this and may need special care.