When it comes to monitoring trademark registers, what you want to search for are newly filed trademark applications that are either identical or way too similar to your existing trademark.
Since your IPO's register is public, you can monitor it yourself regularly. However, this is a rather tedious practice which has to be performed regularly - generally, it's advisable to monitor trademark databases once a month so you don't accidentally miss the other mark's opposition window. If you want to cover multiple countries, you'll have to multiply the effort. And, since you also want to learn about potentially similar marks and not just identical marks, you may not know what similarities to search for.
This is where signing up for a trademark monitoring solution can help. The solution will monitor the register for you and notify you of potentially similar applications.