You can get a small motor bike trailer to do what you want. As it is a trike you will need to either have a flat bed on the trailer or have three tracks lined up with the wheels.
You might be able to get away without ramps or a tilting trailer as you can, if you are able, lift your trike onto the trailer. If not then a means of rolling the trike up will be important.
A small manual/electric winch on the front of the trailer will make the job easier if you have any disability that makes the job awkward.
You could build a trailer, if you have some fabricating skills, or get one built for you, depending on your budget. The trailer will have to meet certain legal requirements for dimensions and lighting. It won't need brakes as it is unlikely to be over 750kg, or the kerb weight of your towing car.
I have four trailers, one is currently on the road, one needs wheel bearings, one needs a spring and the other is still in my workshop. I built three of them and the forth is only for my tractor.
I also build trailers to tow behind bikes.
If you are getting a used trailer it will need to be serviceable. Though there is no MOT test for a trailer there is still a requirement for it to be road worthy and meeting certain regulations. Many old ones on
Ebay don't.
What is your tow car anyway?
You say you have no experience of towing a trailer.
I would strongly recommend getting a few lessons with a driving school and maybe get your B+E entitlement if desired. Towing a trailer isn't difficult but it does take knowledge and experience and so if you know someone who is good with trailers then they can show you what you need to know.
Do some research in to trailers. There is plenty of stuff if you search Google for DVLA driver licence entitlements and trailers, or words to that effect.