I wouldn’t hold my breath. If Winchester, Browning won’t chamber for it, I doubt that Tikka will. I went out to MidwayUSA a few minutes ago and there were 15 different factory offerings from 7 or 8 ammo companies with 125-175 gr. bullets for the 7 REM MAG in stock! I doubt that all of those ammo choices will be available for the 7 PRC anytime soon. A Tikka T3 action isn’t the best to build a long action cartridge on because the action isn’t a long action, it is a “standard length action”. Tikka magazines are tight at 3.34”. Quite a few production rifles are limited to 3.4” mags as well. If all you are going to shoot is factory ammo, then you are stuck with SAAMI COAL spec of 3.34”. If you want to handload you will probably pull the bullet further out of the case and will exceed the SAMMI COAL.
Yes, you can change out bottom metal and run AICS mags but do you really want to? You could get a gunsmith to carve out the action to get 3.6” COAL, if that is your thing. I personally won’t hunt with AICS mags (been there, done that and it sucked!). The only rifle I want to shoot is the Tikka T3. Others around here have had issues hunting with AICS mags, I am not the only one. OP wants to drop into a chassis. The website gives the option for a MDT HNT 26 with a Tikka action that accepts LA AICS mags. It would be interesting to see how MDT is doing it. So far the chassis that I have seen will only accept a short action AICS mag for a Tikka action.
Yes, you can change out bottom metal and run AICS mags but do you really want to? You could get a gunsmith to carve out the action to get 3.6” COAL, if that is your thing. I personally won’t hunt with AICS mags (been there, done that and it sucked!). The only rifle I want to shoot is the Tikka T3. Others around here have had issues hunting with AICS mags, I am not the only one. OP wants to drop into a chassis. The website gives the option for a MDT HNT 26 with a Tikka action that accepts LA AICS mags. It would be interesting to see how MDT is doing it. So far the chassis that I have seen will only accept a short action AICS mag for a Tikka action.