Both the older KeePass databases (.kdb) and the newer (.kdbx) files are still supported in latest version of the program and it can both import and export both versions just fine. No need for a 3rd party utility and quite frankly, there may be no such utility that could convert these files anyway.
Convert KeePass encrypted passwords database to KeePass password database.
We found 2 software records in the database related to .kdb to .kdbx file format conversion.
Microsoft Windows software - convert kdb to kdbx on Windows
Open source easy-to-use password manager
Convert from kdb 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 kdb to kdbx. 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 iOS (iPhone, iPad, iPod Touch devices) software - convert kdb to kdbx on iOS
A secure password storage for iPhone