The act of licking with great enthusiasm, so much that it appears as if the licker is attempting to lift the entire body weight of the lickee using only the tongue.
Analagous to a floor jack lifting a car.
Used for describing the act of cunnilingus or analingus, or non literally as an eager ass kisser or brown noser.
She asked me not to tongue jack her until the friction burns healed.
No need to tongue jack my shitbox, I'll lend you the money.