Someone (typically otherwise single) having extramarital sex with an (often older) partner. Honey is a euphemism for sex and the honey runner often has to run out the back door to escape the spouse. Also using "runner" in the sense of trafficking in something illegal or illicit.
Young Joe is seeing Yolanda behind the back of her husband Terry. I could have told you Joe has always been Yolanda's honey runner.
by Fearman August 01, 2007