Wiktionary
have a finger in
vb. (context informal English) To be concerned or involved in.
Usage examples of "have a finger in".
I realize it wouldn't occur to you, but your super is in a position to have a finger in whatever is going on himself.
He was thought to be rather a dull dog who somehow managed to have a finger in the art pie.
So the one-eyed imp did have a finger in the fantastic thing which had occurred, whatever it was.