As others have said, you will pay tax when you transfer the title. You don?t necessarily have to pay for tags (license plates) though. The seller does not collect the tax. That is done at your local DMV when you transfer the title.
Don't worry. If you received your vehicle title and tags, you can be confident all the legal necessities have been observed.
The point here is that each state has its own tax rules and and a set of procedure for issuing vehicle titles, collecting any taxes or fees that apply, etc. Most of them won't issue the final documents unless and until you can show that all relevant taxes have been paid.
There are two separate taxes collected in KY. Sales tax is paid when you apply for a title. If you already own the trailer, and transfer the title into KY, you must have proof sales taxes were paid in excess of what would be due now, or you pay the tax.
In KY, there is a personal property tax that is due whether or not you license the vehicle, and is collected with the license plate purchase.