Is anyone aware of a company either in Europe or Tallinn specifically that will rent you a TT bike for the race? I see many options for France and Italy but none for the Euro Championship race.
I raced the full there in 2021. I visited a few bike shops in Tallinn (lost my repair kit) which were all very competent, super helpful and most everyone speaks English. Everyone is very friendly. I don’t remember seeing tri bikes at the shops that I visited but I would recommend finding some in the area and calling them and asking if they do rent or know of a place that does. The tri community seemed to be very strong there which was additionally proven by the decent presence I saw of Estonia at Kona this year. Good luck. It’s a great race and an awesome finish line.
I would suggest trying to contact the organisers. They are really nice and resourceful.
I raced in Tallinn in 2021 and KQ. It’s a great race, really well organised.
It would not harm to give the local Tri group a try: https://www.facebook.com/groups/1526146464354783
Similar post are fairly common a few months prior to the event and there is a good chance of finding something.