As long as it is kept sterile, a Tris-HCl buffer is stable for a long time, probably years, at room temperature. Since it is a carbon-containing compound, however, bacteria and mold can eventually grow in it. I keep mine at 4o, where it lasts for years. If you keep it frozen, it will probably last essentially forever.

Tris-HCl at pH 7.2 is as useless as my answer

Omar Gonzalez-Ortega makes a good point. The pKa of Tris is about 8.1 at 25oC, which means that it has little buffering capacity at pH 7.2, especially for acids. HEPES or MOPS or phosphate buffers would be better choices for pH 7.2