Give A Shite Meaning

(idiomatic) To care; mind; consider important

Example: 1922, James Joyce, Ulysses Episode 16
  I'd carry a sandwichboard only the girl in the office told me they're full up for the next three weeks, man. God, you've to book ahead, man, you'd think it was for the Carl Rosa. I don't give a shite anyway so long as I get a job, even as a crossing sweeper.