How does aqueous ammonia react with hypochlorous acid in water?
Yes, aqueous ammonia will react with hypochlorous acid to form chloramine gas as suggested by @Waylander. But the reaction will also form an intermediate product i.e  ammonium hypochlorite($\ce{NH4ClO}$).

$$\ce{HClO + NH3•H2O → NH4ClO + H2O}$$


  Hypochlorous acid react with ammonium hydroxide to produce ammonium
  hypochlorite and water. Ammonium hydroxide - diluted solution.(chemiday)


The mechanism of this reaction is explained in this Reddit post. You will find the insight of the post useful. I am just pointing out one information.


  Ammonia solution and hypochlorite react (in solution) to produce toxic
  chloramine gas. Ammonium hypochlorite is also formed during the course of
  the reaction, but it decomposes somewhat rapidly to chloramine.


I am assuming this is an exercise question. Do not try to attempt this reaction if you are not an experienced chemist as it also produce deadly byproducts like chlorine gas, hydrazine, dichloroamine and probably nitrogen trichloride. Chloramine is itself poisonous.