Lazio, which includes the city of Rome has reported new cases as of yesterdays and will slowly ban arriving flights at the airports along with other lockdown and travel restrcitions.
Alessio D’Amato, Lazio’s Health Commissioner had reported 17 new COVID-19 cases on Sunday. 10 of these cases were foreign residents who had returned to Italy from being abroad.

Rome has seen many of its Bangladeshi residents return to Italy with the coronavirus and therefore have now banned arrivals at Fiumicino Airport from 13 at-risk countries which include Bangladesh.
If more cases are found within this region of Italy it is possible that previous and strict lockdown rules could be put back in place until cases lower.
Sources:
[Euro Weekly News]
[The Telegraph]