The Thirteenth Doctor claimed to be a doctor of, among other things, engineering. (TV: The Tsuranga Conundrum)
The Kaled Varna was a student of engineering, being able to use her skills to quickly deduce the power functionality of a Dalek War Machine. (AUDIO: The Lights of Skaro)
Among Time Lord culture, the study and manipulation of stars was referred to as stellar engineering. (PROSE: Original Sin) The Eleventh Doctor cited his TARDIS' Eye of Harmony as an example of "Time Lord engineering". (TV: Journey to the Centre of the TARDIS) Time Lords were also capable of manipulating matter at a scale lower than the molecular, a process known as quantum engineering. (COMIC: The Lost Dimension)
In the Federation universe, Montgomery Scott was the chief engineering officer aboard the USS Enterprise in the 23rd century. In the 24th century, Geordi La Forge served the same role aboard the USS Enterprise-D. (COMIC: Assimilation²)