Hello, my last Minecraft account was hacked, but it was not possible to restore it, because the Transaction ID was lost due to the fact that I changed the payment system. So I bought a new Minecraft (with the same nickname), and all the things, including my TARDIS, were lost. Can I transfer them to a new account?

If you have proof it was you older account,
Here are some great things to use - 
If you linked your SWDTeam account with old MC account
Being on the same network on the old account if you cannot reach it through the launcher

Yes, I connected the old Minecraft account, but I have already replaced it with a new one. If that I belong to a clan "The republic of eldiena"

The first time I synced Minecraft account on the day the swd team account was created, July 13, 2021. And the new Minecraft account is on August 14, 2021. The last time I logged into the server from my old account was August 2, 2021.