Right, as I understand it, the "economic rent" (ER) of an apartment lease would be the extent to which the cost of the lease was inflated by artificial scarcity (as opposed to just supply and demand). There are, then, rent-seeking things you could do as a landlord/developer, but in a well-functioning market where you're competing with lots of other landlords, the price of a lease reflects the market value of occupancy and does not include ER.

Similarly, one of the classic examples of ER is wage premiums paid to closed-shop union members: the clearing price for the labor involved is, say, $20, but your union bumps that up to $25; the extra $5 is ER. There is directly substitutable labor that could be acquired at a discount to union labor, but closed-shop rules lock in the extra rents.