$string="Referring Hospital Triage Time <183> 2 h (N <26> 191)"; 
$pre_str="Referring Hospital"; 
$str1=$string;
$str1=~s/\Q$pre_str\E//;

print $str1;
[download]

prints

 Triage Time <183> 2 h (N <26> 191)
[download]