If i wanted to simply redirect /clients/page/ to /clients.php?view=page i would use something as simple as this, it works great.
/clients/page/
/clients.php?view=page
Option
I think you can use the [QSA] flag, which stands for Query String Append. This means that you can add variables to the Query String easily:
RewriteRule ^clients/([^/]+) /clients.php?section=$1 [QSA, NC]