Scientific advisor was the title given by UNIT to their personal adviser on science and technology-related matters.
In the 1970s, the British branch of UNIT originally selected Liz Shaw to be their scientific advisor, but this role soon went to the Third Doctor, with Liz staying on as his assistant. The Doctor served as UNIT’s scientific advisor throughout his exile on Earth. (Spearhead from Space onwards) Although the Doctor ceased to stay on Earth on a regular basis after he regenerated into his fourth incarnation, his affiliation with UNIT remained, with others such as Colonel Mace noting that the Doctor had never officially resigned his position. Robot, The Sontaran Stratagem) Even when not actively working with UNIT, the Doctor wasn’t above using his UNIT credentials to establish authority to investigate such matters as disappearing Concordes (Time-Flight). Even in 2001, the Doctor retained a legendary reputation among UNIT, with the Brigadier musing that a three-second silence after learning that the Doctor was present during a crisis was an impressive incident (The Shadow in the Glass).
In the 1990s, Iris Wildthyme was UNIT’s special scientific advisor. (Interference – Book Two, Bullet Time)
By 2010, UNIT’s regular scientific advisor was Malcolm Taylor. (Planet of the Dead)
The Intrusion Countermeasures Group, a predecessor to UNIT, had a “scientific advisor” role as well. In 1963, Rachel Jensen filled it. (Remembrance Of The Daleks)
Joking, the Fourth Doctor offered Duggan a position as his scientific advisor. (City of Death)
While investigating the strange abilities of apparent medium James Lees for Queen Victoria, the Fifth Doctor was officially appointed Queen Victoria’s scientific advisor, being offered to remain in the role even after his departure (Empire of Death).
A clone of the Sixth Doctor served as the Forge’s scientific advisor from 2004 to 2008. (Project: Lazarus)
On Hellcombe Factory, the Eleventh Doctor claimed that Corporal Edward Anderson was his scientific advisor. (The Dalek Project)