To have something covered. To take care of business. To have everything under wraps.
Complete.
No need for alarm.
"You need help moving? Your dad needs a kidney? Your girlfriend needs to be picked up at the airport? I got all this, bro. Comp the bar!"
"Hey, buddy. I didn't mean to spill that beer on you. It's all good. Comp the bar, man... comp the bar."
After getting laid: "Comp the bar!"