To push a new local branch to a remote Git repository and track it too, you can follow these steps:

1. First, make sure you are in the local branch you want to push to the remote repository.

2. Use the git push command with the -u or --set-upstream option followed by the remote name and branch name. For example, if the remote name is "origin" and the branch name is "new-feature", you would use the following command:

git push -u origin new-feature

3. This command will push the local branch "new-feature" to the remote repository named "origin" and set it up to track the remote branch with the same name.

4. Once the branch is pushed and tracked, you can use the git pull command to fetch and merge changes from the remote branch and use the git push command to push changes to the remote branch.

5. Finally, you can switch to the new branch on the remote repository using the git checkout command. For example:
git checkout new-feature

That's it! Your new local branch has been pushed to the remote Git repository and is now being tracked.