Originally, UNIT had no time travel capability. While the Doctor was still working for UNIT after the Time Lords lifted his exile at the end of "The Three Doctors", he did have time travel capability & could take UNIT personnel with him, when necessary. After that, UNIT again had none.
At some point (we don't know just when), Jack Harkness gave UNIT his vortex manipulator, as revealed by Kate Stewart to Clara Oswald in "The Day of the Doctor". UNIT then did have time travel capability, although it was kept secret (especially from the Americans) & we don't know if it was ever used.