Technical Services Officer was a title borne by some Imperial Navy personnel serving with the Technical Services division of the Fleet Support Branch, the part of the Navy responsible for all aspects of shipboard maintenance that did not involve main engines or hull integrity.
For example, in 3 ABY, Commander Brandei was serving in the role of Technical Services Officer aboard the Super Star Destroyer Executor. He had a station in one of the crew pits on the bridge, and he is known to have been in charge of maintaining the ship's TIE Fighter squadrons.
It is not entirely clear whether the title of "Technical Services Officer" indicates the senior Technical Services officer aboard a specific ship (in which case maintaining the TIEs would only have been a small part of Brandei's role) or whether it was a generic title for Technical Services personnel.
No specific position of Technical Services Officer is known in the chain-of-command of escort frigates, where both the main Technical Services specialities, Power and Life Support, came under the authority of the Engineering Department, representing the other primary division of Fleet Support Branch. However, the Power Chief was also subordinate directly to the ship's Operations Officer for some purposes, and it is possible that one or other of them was performing the role of Technical Services Officer.