redirect using htacces domain.com/old_site to domain.com/new_site

I have changed one of my sites name from "http://www.domain.com/old_site" to "http://www.domain.com/new_site" (and some time ago it was "http://old_site.domain.com/")

How can I make htaccess redirect all old links?
I tried:

RewriteCond %{HTTP_HOST} ^old_site.domain.com$ [OR]
RewriteCond %{HTTP_HOST} ^www.old_site.domain.com$ [OR]
RewriteCond %{HTTP_HOST} ^www.domain.com\/old_site$ [OR]
RewriteCond %{HTTP_HOST} ^domain.com\/old_site$
RewriteRule ^/?$ "http\:\/\/www\.domain\.com\/new_site\/" [R=301,L]

Basically I want all old links to continue working.

Any hint is welcome.

Thanks