CodePudding user response:
You can repeat matching 0-3 times including the > using
^(?:[^>]*>){0,3}[^>]*
^Start of string(?:[^>]*>){0,3}Repeat 0 - 3 times matching any character except>and then match>[^>]*Optionally match any char except>
See a regex demo.
If there should be at least a single > then the quantifier can be {1,3}

