Redirect all links form a category to new links on new category

Using Apache

I’d go with an .htaccess rule

RewriteRule ^test/(.*) http://www.example.com/demo/$1 [R=301,L]

so http://www.example.com/test/page would now go to http://www.example.com/demo/page and the 301 redirect would make it permanent

make sure you put your rewrite rule after these rules

RewriteEngine on
RewriteBase /

Using Nginx

in the server block

server {
  . . .
  rewrite ^/test/(.*) http://www.example.com/demo/$1 permanent;
  . . .
}