Is it permissible to work for a real estate company if its capital is shared between the government and a bank, knowing that the bank has no relation to the operations of the company that manages properties received from the government?

We have no knowledge of the nature of the real estate company mentioned. If its capital is mixed, containing both permissible (government contribution) and impermissible (contribution from a usurious bank) elements, then there is no harm in working for it, provided that its field of work is permissible.