Sustainability competence is understood as the interlinked set of knowledge, skills, attitudes, and values that effectively enable embodied action in the world concerning real-world sustainability problems, challenges, and opportunities, according to the context. Higher education institutions should promote this competence in their graduates due to its importance, which has been stressed during the period of COVID-19. However, it seems to be becoming forgotten, in the syllabus as well as in the voices of teachers and students. A study carried out at the University of Barcelona (UB) with n = 265 students and n = 129 professors on the importance and frequency of assessing this competence in times of pandemic is presented. Quantitative data was supplemented with n = 31 interviews. The data show a scarce use of assessment strategies to evaluate this competence (9.7% of the students and 15.2% of the teachers indicate some type of assessment) as well as a very low consideration of the usefulness of the assessment processes of this competence. Interviews prove that this is a missing competence. However, 14% of the students associate it with productive assessment tasks, and 19.4% of the teachers think it is related to well-aligned assessment tasks. Therefore, it seems that the future challenge is in the design of learning and assessment tasks which should consider sustainability in teaching plans and ask students to apply, solve or make decisions considering environmental, social or economic sustainability.