Probably not exactly the same film as TX400 but hard to tell because "Tri-X" had a number of formulations over the years and also varied somewhat by format.
It the box is marked ISO 400, I'd expose it at ISO 200 and develop for 7min in HC-110 Dil. B agitating initially for 30 seconds and then 5 seconds every 30 seconds thereafter. However, film this old is more likely to be ISO 320, so check the box. If so, expose at ASA 160 and develop as above.
I've also had very good look with semistand processing old Tri-X. You'll need a Nikkor stainless reel and a way to suspend it off the bottom of the tank - an inverted small funnel will do. I expose at full ISO and dilute Pyrocat-HD 1.5:1:250. I do an initial prewet of 3 mins, followed by 2min continuous agitation in the developer, let it stand, 10seconds of agitation at 31min, pull and stop/fix at 60min.
Alternatively, you can follow the same seminstand regimen but use D-23 1:3 instead.
You will likely see some fog with any of these developers, but the Pyrocat will show the least amount of visible grain when printed/scanned. The D-23 will probably produce the least amount of fog.
I have processed Tri-X from the 1970s this way and gotten quite reasonable results. The one caveat is if the film has been subjected to wild temperature swing, it can incur mechanical failures like emulsion chipping.