Design Pro used both .zdl and .zdb files for its label designs, with .zdl files being used in the newer version of the program. We couldn't successfuly verify, whenever Design Pro is backwards compatible and allows users to save their new designs to older version. In any case, your best (and probably only) option is Design Pro.
Convert DesignPro label design to DesignPro label design.
We found 2 software records in the database related to .zdl to .zdb file format conversion.
Microsoft Windows software - convert zdl to zdb on Windows
A software for Avery label design and printing
Convert from zdl file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned zdl to zdb. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert zdl to zdb on OS X
Program for control all Avery products and create documents