It sounds like you are looking for do_action()
In your method that you wrote add do_action and it will trigger your new custom action. Then you can use add_action()
in the same way you use the build in actions.
https://developer.wordpress.org/reference/functions/do_action/
Example of your method in the class…
public function some_method() {
$foo = 'puppy';
$bar="bunny";
do_action( 'my_nifty_action', $foo, $bar );
}
Somewhere else you can then add the call to your action…
add_action( 'my_nifty_action', 'my_custom_function', 10, 2 );
function my_custom_function( $foo, $bar ) {
// ... your code here
}