This is the 12607th most frequent Russian word.
консульские
"Consular" – relating to a consulate or consuls.
The word 'консульские' is used here as an adjective to describe the type of services being provided, specifically those related to the consulate.
Консульские услуги предоставляются в консульском отделе.
Consular services are provided in the consular section.
In this sentence, 'консульские' describes the subject of the discussion—questions or issues pertaining to consular affairs.
На приёме обсуждали консульские вопросы.
During the meeting, consular issues were discussed.
Here, 'консульские' modifies 'обязанности' (duties), indicating that the duties are associated with consular responsibilities.