The system already does this, though there are a few things you can do in addition.
First and foremost, every edit to a post, new answer to a question or several other actions will bump a post to the top of the home page. This means that everyone who visits that page will see your new post (and can navigate directly to the change by clicking the time stamp).
Additional things you can do is come to chat and talk about your new answer, add a bounty to the question to put it in featured questions (though really this is sort of silly for you to do as an answerer since you can't give the bounty to yourself). Finally you can promote the question and it's answers in other forums.
So pretty much, the system automatically should be putting some community eyes on every new post.