Replacements in the Red Army were given out when the unit in question was out of battle. If you're a commander of a T-34 tank in 1944, odds are you're engaged in a very long offensive operation, so you're not going to see any new tanks until you're in a lull between battles. Once you get to that, it depends on how well off your unit is. If it's still in pretty good shape, you have a pretty low chance of getting a brand new tank unless yours was lost in battle. Fairly early (1942-43 production) T-34 tanks still popped up in photos from even the spring of 1945. Award orders for mechanic-drivers make a special point to point out how many thousands of kilometers the driver's tank travelled for, so your odds of getting a new tank if your current one works fine are slim.

Naturally, if you lose your tank (either in battle or to mechanical failure) and make it back to base in one piece, you get a new one. This might not have been the case in desperate days of 1941 where even tankers were used as ersatz infantry when not a single man could be spared, but in 1942 a huge effort was undertaken to prevent anyone trained in use of tanks from being assigned to a non-tank related task. "Unhorsed" tankers would be given new tanks when their brigade was in a position to receive shipments by rail. In some cases skeleton crews would be sent to the nearest railway station to receive a shipment and drive it back to the brigade's location on their own. Now, getting a new tank doesn't mean you get a new tank. Even as late as 1944 you could end up with a gently used Matilda or some other less than glamorous vehicle, even if your comrades are all driving around in shiny new T-34-85s.

If your brigade gets absolutely mauled, this is your chance to get a new tank even if yours is still working. Units with just a handful of tanks left could be withdrawn entirely for refilling and training. In this case, you hand off your remaining materiel to another unit before you go. This is your best chance of getting rearmed with brand new tanks, although there was no guarantee that this would be a T-34-85. Specifically in 1944 as shipments of Sherman tanks picked up your unit might find itself using Shermans/Valentines instead of domestic tanks.

http://www.tankarchives.ca/2016/01/lend-lease-trade-in.html

https://warspot.ru/16203-novorossiyskie-shermany

https://warspot.ru/16407-shermany-na-kurskoy-duge

http://www.tankarchives.ca/2015/06/common-questions-sherman-preference.html