My house rental agreement will expire soon and I have to shift to a new house. Can I do this during Moharram as long as it is not on the day of Ashura?
Bismihi ta'ala
There would not be any shar'i problem with changing places, as long as there is no intention in desecrating the sanctity of this holy time of mourning.
It would be advisable, if it is possible, to postpone until after Ashura, and to continue to allocate time for your 'azaa` and dedication in mourning for Imam Husain (a.s.).
With prayers for your success.