Thanks for the link! Earlier, we read that "It was from journalism that Walter had graduated to the eminence of radio commentator."
"Air" can mean "radio" ("the airwaves" being another way of saying "radio waves.")
"Before you took to the air" means "before you became a radio commentator," i.e. before you were became somewhat famous.
"Get-out" isn't familiar to me--I'm from the U.S. and this might be a British expression--but the meaning is clear.
Debham's was his publisher. He has written a new book. He ought to offer it to Debham's. Perhaps he has a contract with them that gives them "right of first refusal." He doesn't want to offer it to Debham's because he doesn't like the way they handled his farm book. He needs an excuse, something way _to get out_ of his contract. He can use their rejection of his poems as the excuse--"the get-out"--he needs.