I've just stumbled across this article, which states that direct services between Tallinn and Riga started on Monday. No change in Valga required, with the unit (an Elron FLIRT) travelling down to Riga in the afternoon and returning the following morning.
Rough translation below:
The timetable is also available here. This now has the quirk of meaning that the Valmiera-Riga route in Latvia now has a train from each of the three Baltic operators on it (the Vilnius-Valga service being a Lithuanian LTG Link unit).
Rough translation below:
On Monday at 2:50 p.m., the first Tallinn-Tartu-Riga route departed from Balti Jaam in Tallinn, arriving at Riga Central Railway Station on Monday evening at 8:46 p.m.
Initially, international tickets will be sold for the route, while domestic Latvian tickets between Valmiera and Riga will be offered in the coming weeks, Elron announced.
From January 12, the Tallinn–Tartu–Riga train will depart from Tallinn at 2:50 p.m., from Tartu at 5:05 p.m., and arrive in Riga at 8:46 p.m. The train will depart from Riga at 7:38 a.m., arrive in Tartu at 11:25 a.m., and arrive in Tallinn at 1:57 p.m. The first departure in the Riga–Tartu–Tallinn direction will be on January 13 at 7:38 a.m.
According to the current timetable, the Tartu–Riga trip takes 3 hours and 41 minutes, the Tallinn–Riga trip takes 5 hours and 56 minutes.
A ticket from Tartu to Riga costs 19–22 euros, from Tallinn to Riga 29–32 euros. The route is operated by two-car Stadler Flirt diesel trains.
One train a day, which runs to Riga in the evening and back in the morning, is estimated to require about one million euros in state subsidies per year.
The Tallinn-Tartu-Riga train line was launched in cooperation with the Ministry of Climate, the Ministry of Regional Development and Agriculture, the City of Tartu, the Latvian passenger train operator Vivi, and other Latvian partners.
The timetable is also available here. This now has the quirk of meaning that the Valmiera-Riga route in Latvia now has a train from each of the three Baltic operators on it (the Vilnius-Valga service being a Lithuanian LTG Link unit).