In spaceflight keeping track of time between systems widely separated in space (e.g. people on Earth vs spacecraft in deep space) and/or time, moving at substantial relative velocities and in different gravitational potentials is a challenge.
The documentation for JPL's Horizons at https://ssd.jpl.nasa.gov/?horizons_doc includes the following discussion of timescales.
The three time systems are described as follows:
("Barycentric Dynamical Time"); typically for cartesian, osculating element, and close-approach tables. The uniform time scale and independent variable of the planetary ephemeris dynamical equations of motion.
("Terrestrial (Dynamic) Time"), called TDT prior to 1991, used for observer quantity tables. This is proper time as measured by an Earth-bound observer and is directly related to atomic time, TAI. TT periodically differs from TDB by, at most, 0.002 seconds.
is Universal Time This can mean one of two non-uniform time-scales based on the rotation of the Earth. For this program, prior to 1962, UT means UT1. After 1962, UT means UTC or "Coordinated Universal Time". Future UTC leap-seconds are not known yet, so the closest known leap-second correction is used over future time-spans.
Different time scales are managed differently, and some are updated and/or corrected relative to others from time to time (pun intended).
Question: When and for what purpose is TAI updated? (not about a one-second error)