"It's a contemporary story of an estranged father/ crime figure who returns to help his son, who has been set up for a crime he did not commit," said extras co-ordinator Stephen Kirk.
"We're starting filming The Returnon October 13, and we'll finish on Saturday, December 13 and we hope to give people the opportunity to rub shoulders with a host of A-List celebrities."
The four-part drama is set in Co Wicklow, Dublin and Manchester, and hundreds of extras are needed over the course of filming.
Cast members include Desperate Housewives' Dougray Scott, who played Ian Hainsworth.
Actress Sophie Okonedo, who starred in the Oscar-nominated drama Hotel Rwanda, will also be playing a leading role in the drama.
The casting crew say they are looking for people "from all ages and many culturally diverse backgrounds -- especially black and Asian."
"The extras will be on set at the same time as the cast members," added Mr Kirk, who says the chosen extras will get to work with these big names, so it won't just be a "meet and greet".
"We're looking for hundreds because we're filming across nine weeks.
"There'll be standard extras standing in the background. But then we'll be filming scenes in a prison, a school, and a hospital and we'll be casting extras for those scenes."
Successful applicants may end up working for a number of days on the drama.
"Some will be used more than once, and some will come in for one day.
"We'll have standard extras, featured extras with a special role, and speaking extras," he added.
Mr Kirk said the extra parts might suit those wishing to gain experience in acting, or those who are thinking about enrolling in an acting course.
The extras department will be holding two open casting sessions, both at Liberty Hall, Eden Quay, Dublin 1 (SIPTU building) on Thursday October 2 and Friday, October 3 between noon and 7pm.
"You'd never know what might happen," Mr Kirk said.