How do I rewrite the below...
There's possibly a more fundamental problem here. You don't rewrite it that way round in .htaccess. You rewrite from the "friend" URL back to the actual URL/filesystem path. So, it's the other way round, you rewrite from:
http://example.com/local/vendor/Company
to the actual URL your application is expecting:
http://example.com/local/vendor/index.php?handle=Company
For Example:
RewriteEngine On
RewriteRule ^(local/vendor)/(Company)$ /$1/index.php?handle=$2 [L]
$1 and $2 are backreferences to the captured groups in the RewriteRule pattern.
The above matches just the specific URL you stated, ie. /local/vendor/Company. I suspect that "Company" is intended to be a placeholder? In which case you need to make this more general. For example:
RewriteRule ^(local/vendor)/(\w+)$ /$1/index.php?handle=$2 [L]
\w is a shorthand character class for word characters. This excludes the dot (ie. .) so avoids a rewrite loop when rewriting to index.php.
UPDATE: The above assumes your .htaccess file is located in the document root, ie. example.com/.htaccess. However, if the .htaccess file is located in the /local subdirectory (ie. example.com/local/.htaccess) - as you appear to suggest in comments - then you will need to adjust the above directives to remove local/ from the RewriteRule pattern and remove the slash prefix from the substitution. For example:
RewriteRule ^(vendor)/(\w+)$ $1/index.php?handle=$2 [L]