izdavati

1. (of housing, premises) to rent out; to let
   Izdajemo stan studentima već pet godina. — We've been renting our flat out to students for five years.
   Izdaje se garsonjera u centru grada. — Studio flat to let in the city centre.
2. (of documents, orders, medicine) to issue; to give; to dispense
   Opština izdaje izvode iz matične knjige rođenih. — The municipality issues birth certificates.
   Samo on ovde izdaje naređenja. — He's the only one who gives orders here.
   Apoteka izdaje ove lekove samo na recept. — The pharmacy dispenses these medicines by prescription only.
3. (of books, magazines) to publish
   Ova kuća izdaje uglavnom knjige za decu. — This publisher mostly publishes children's books.
4. (of a person, memory, strength) to betray; to fail
   Pravi prijatelj te nikad ne izdaje. — A true friend never betrays you.
   Pamćenje me sve češće izdaje. — My memory lets me down more and more often.
5. (izdavati se za) to pose as; to pass oneself off as
   Prevarant se izdavao za policajca. — The con man was posing as a police officer.
6. (of signs, behaviour) to give away; to reveal
   Naglasak ga izdaje. — His accent gives him away.
   Ruke joj drhte i izdaju njenu nervozu. — Her hands are trembling and give away her nervousness.

The perfective is izdati. 'To rent from someone' is iznajmljivati or unajmljivati (imperfective) and iznajmiti or unajmiti (perfective), not izdavati / izdati.