Once you've done your initial check and have decided that you're not preempted, schedule regular alerts to inform you of any newly-published articles on your topic. If a preempting article appears while you are writing, it's best to know sooner rather than later.
Most article-finding tools in any scholarly discipline will let you set up searches to run automatically, and will send you emails notifying you of new results.
Consider setting up alerts in the following sources. The first five sources give good coverage of law review articles. Use Google Scholar and the Gleeson Library databases when you have an interdisciplinary topic.
Current Index to Legal Periodicals using Westlaw's WestClip.
Index to Legal Periodicals & Books. Use the alerts function provided on the publisher's web site.
HeinOnline's Law Journal Library using the MyHein feature to save searches so you can run them later.
The "full text" law review article databases on Lexis and Westlaw.
Google Scholar using the "create email alert" function.
Non-Legal Article Databases from the Gleeson Library Databases collection. (Each of these will have its own method for saving searches and creating alerts.)
Citations to newly-published law review articles often show up in Current Index to Legal Periodicals (CILP) before they appear anywhere else. A weekly Westlaw WestClip is a good way to monitor CILP.
On Lexis and Westlaw, it's easy to set up regular alerts. You can use alerts to check for new articles in any of the "full text" sources. The two-page guide "Lexis Alert & WestClip instructions" takes you through the process.
HeinOnline does not yet have an email alert function. But you can use the MyHein feature to save searches which you can then run at any time to update your research. The "Cheat Sheet" for HeinOnline's Law Journal Library explains how to set up a MyHein account and use it for saving searches. (MyHein is available at no charge to USF faculty, students, and staff.)
Google Scholar (like many other Google search products) lets you set up email alerts. The "Alerts" section of Google Scholar's search tips explains how.