Is it permissible for an agent who does something on behalf of another to take payment for his work?
It is permissible to appoint an agent with or without payment. The evidence for appointing an agent without payment is that the Prophet (peace and blessings of Allaah be upon him) appointed Unays to carry out the hadd punishment on a woman, and he appointed ‘Urwah al-Baariqi to buy a sheep, without paying them for that. There are many similar examples in the ahaadeeth apart from those that we have mentioned.
The evidence for appointing an agent with payment is the aayah (interpretation of the meaning):
“As-Sadaqaat (here it means Zakaah) are only for the Fuqaraa’ (poor), and Al-Masaakeen (the poor) and those employed to collect (the funds)…”
so those who are appointed to collect and distribute the zakaah are given a share of it as you can see.