fish shop; fishmonger; fish dealer
Refers to both the shop that sells fish and the person who runs it. Context usually makes the meaning clear.
I bought fresh sashimi at the fish shop in front of the station.
That fishmonger is always cheerful and gives me a little extra.
I bought some fresh fish at the fish shop nearby.
My father runs a fish shop near the station.
He says he wants to become a fishmonger in the future.