The Chlorine is the oxidizing agent. The Bromine is the reducing agent.
Cl goes from a zero charge to a -1 charge The chlorine has been reduced its charge has gone down.
Br goes from -1 to a zero charge. The Bromine has been oxidized it charge has gone up
And if we assign oxidation numbers, we can immediately see the direction of electron transfer:
Bromide ion has been oxidized; chlorine gas has been reduced. Note (i) that you simply must know that the halogens are normally bimolecular; we represent them as
Also note (ii) that we probably could not get this reaction to work, even if thermodynamics is on our side.