TAI is independent of the altitude.
The clocks that were used to build TAI (its a co-ordinated average of dozens of atomic clocks around the world) became sufficiently accurate that the difference in each second based on the altitude of the clock measuring it in the early 70s. As a consequence of this it was decided that as of 1 January 1977 00:00:00 TAI would be corrected to correspond to what TAI should be if measured by clocks at the geoid (mean sea level) and as a result it has no relation to altitude or accelerations. There is also (because metrologist are like this sometimes) a continually published version of what TAI was before 1 January 1977 00:00:00 but it is now named EAL (Échelle Atomique Libre, meaning Free Atomic Scale)
In addition to this, we have already designed and maintain equivalent time standards to TAI, but for the Earth's barycentre Geocentric Coordinate Time (TCG - Temps-coordonnée géocentrique) which is roughly speaking TAI for a clock orbiting the sun, where the earth moon barycentre orbits, but without the earth & moon gravitational influence... and for the entire solar system Barycentric Coordinate Time (TCB, from the French Temps-coordonnée barycentrique) which is roughly speaking again, equivalent to a TAI style clock but this time subtracting the entire solar system, as if a clock keeping TAI was just orbiting the galaxy at the barycentre of the entire solar system.
The cutting edge of this is building up astronomical data on ultra stable pulsars to use as "external" reference clocks far outside the solar system, but the complexities of subtracting the effect of all the universe the pulsars' radiation beams pass through before they get to us, makes it quite challenging. But the utility for deep space navigation has made it an active funded path of research for at least the last decade. (to get a GPS equivalent at lunar distance and beyond where it becomes rapidly impractical to have a GPS like orbiting constellation due to inverse square radio broadcast power limits, good radio can pick up GPS at the moon but the location precision out at that distance... is not great)
The cosmic microwave background dipole may be indicative that we can use it as an absolute frame of reference but settling that with enough certainty to base an official time standard on it, seems like some time away based on the state of things between cosmology, astronomy, astrophysics and metrology.