Sims will need to build skills such as logic and charisma to progress through the Mortician career. Sims will go to work in their own clothes, however you could always use CAS to create a 'work' outfit you think is suitable to change them into before work. The job is available with other jobs via the 'find a job' interaction.
This is a new career for the sims 4: Mortician! Your sims can progress up to level 10 of this career.