This clip is from an episode of The Allusionist, which is a wonderful podcast all about language.[adrotate group="2"]
The speaker is talking about his work as a hand engraver – cutting text or designs into objects (usually jewellery) by hand. The speaker has a London accent.
About the sentence
…it’s a dying trade…
If someone refers to a job or profession as a dying trade, then they are saying that it is disappearing due to a lack of demand or need for it.