You could always use [man]strpos/man to find the first offset, then +4 that offset and use [man]strpos/man to find the second, and then [man]substr/man from that offset +4 to the end, then use strip_tags.
The "+4" is because "</a>" is 4 characters long. So we get the position of the "<" character, then add 4 to move the marker to the character after the ">".
Something like:
$string = 'This text has <a href="#">1 link</a>, <a href="#">2nd link</a> and a <a href="#">3rd link</a>.';
$first_link = strpos($string, '</a>');
$second_link = strpos($string, '</a>', $first_link+1);
$string1 = substr($string, 0, $second_link+4);
$string2 = substr($string, $second_link+4);
$string = $string1 . strip_tags($string2);
echo $string;