1
general::
Have a means of gaining advantage with, have influence on, as in She had pull with several of the board members. [Colloquial; late 1800s]
American Heritage Idioms
2
general::
Phrase(s): have pull with someone
to have influence with someone. (Also with some, much, lots, etc.) • Let’s ask Ann to help us. She has pull with the mayor. • Do you know anyone who has some pull with the bank president? I need a loan.
McGrawhill's American Idioms And Phrasal Verbs