In our research area, when we are going to evaluate forest products produced and sold around the world, we usually use FAOSTAT. Are there other databases (in addition to FAOSTAT) that bring this information?
I believe that for the EU area, EUROSTAT can be a valuable option since it draws data directly from every member country. However, there might be some holes due to countries not updating their national data yearly.
For some countries, their national statistic services are more updated than the DB present at FAOSTAT, so I suggest you to give it a shot as well if needed.
This may be useful to you: https://ec.europa.eu/eurostat/data/database
Hei Elias - in addition to Alberto's suggestions have a look at UN Comtrade data - this can show trade in wood products to HS code 4 digits if I remember correctly. As Albert also suggested for EUROSTAT - there are issues with this kind of data.
There are also other trade databases that may be relevant - Trade Data Monitor (TDM), Panjiva, export/import genius - while these have more details (e.g. TDM shows port/province of entry) they only cover limited number of countries.