A piece / slice of the action: it's a slang = when someone wants to be involved in something successful that someone else started. It's a share in a scheme, project or profits; a share or role in an interesting or exciting activity, especially in order to make money: 'If you guys are going to bet on the football game, I want a piece of the action, too.' 'Cut me in for a piece of the action.' cut somebody in = to give sb a share of the profit in a business or an activity

Hello Nydia, If someone wants to 'have a piece of the action' or a slice of the action, they want to take part in an exciting activity or situation, usually in order to make money or become more important. You can use " a piece of" with many uncountable nouns to refer to an individual thing of a particular kind. "Action" here as an uncountable noun means doing something for a certain purpose. So someone is asking another to do something , to act in a particular situation or activity pursuing a certain purpose ( making money / becoming important etc ..), that is surely apparent in the context of the paragraph.