Learn Italian: Il capo deve assegnare un nuovo compito a Marco. - The boss must assign a new task to Marco.

You would add the iterative prefix ri- to the verb assegnare, making it riassegnare. The sentence would become Il capo deve riassegnare un nuovo compito a Marco. The prefix ri- is widely used in Italian to indicate doing an action again, just like 're-' in English.

Why is nuovo placed before compito here instead of after it?

Placing nuovo before the noun means 'new' in the sense of 'another' or 'an additional' task. If it were placed after the noun (un compito nuovo), it would emphasize that the task itself is completely original or brand new in its characteristics.

Could I use lavoro instead of compito for 'task'?

You can, but compito is much more specific to a 'task', 'assignment', or 'duty' given to someone (it is also the word for school 'homework'). Lavoro is broader and usually translates simply to 'work' or 'job'.

If we replaced a Marco with a pronoun to say 'assign him', where would it go?