What Happens When You Launch a New Site Section?
If there's a close relationship between your new site section and the historical trusted aspect of the site, you'll likely pick up some traffic quite quickly. However, sites stall a bit after that. They get a little taste of the good traffic for their new section, but then it stops growing.
Over a period of time, it will remain frozen, but then if you're doing the right things (developing quality content, link building), you may see a jump in traffic. My own conjecture is that a combination of quality inbound links and time raises the trust level of the new site section.
Once you cross a trust threshold, you enable a new period of growth until you hit the next threshold. Then the cycle repeats. I've seen this behavior several times now during the development and promotion of new sections of content on existing sites.
How Can You Speed Things Along?
We already mentioned the two most important things above. Developing quality content was one of them.
While search engine crawlers can't measure content quality in a direct sense, they can understand the relevance and depth of a Web page, provided you put enough text out there for them to chew on. Also, if a new site section is really thin on content, you can send negative signals to the search engines.
The other thing you need to do? Our old friend, link building. At least some of the signals for evaluating trust are based on link analysis. Getting high quality links from high quality sites will help you establish that trust.
The above is a sandbox scenario, but applied to new content section on an existing site, it operates much the same way. You benefit from the inherent trust of the existing domain, but still need to prove it to the search engines by getting new links to the new section itself.