I recently converted a Drupal 6 contributed module to Drupal 7 for one of my client project. I would like to contribute this converted module to the community. How to upload this in the existing project page? Do I have to create a patch or will it be a sandbox project?
For this you need to create a sandbox project and open up an issue in the issue queue of the existing module, posting a link there and urging the maintainer of that project to have a look.
If they wish, they can commit that module as the official 7.x version, or might even add you as a co-maintainer of the module if you are interested. In case they do not find this module interesting, you can create it as a separate project: Create the sandbox, apply for project application approval in the Drupal.org project approval queue, and get this published as independent module.
I'd probably create an issue in the existing project page, and upload as a patch there.
@Chapabu's sandbox suggestion IMO is an optional extra. The main thing is creating the issue so it's visible to the community. A patch is fine (although having ready access to a tarball is a good feature for facilitating testing by others).
If the D6 project is not upgraded to D7 by now, you might find the maintainer is no longer engaged with the project.