On the up and up and Up-and-coming

Up-and-coming and on the up and up are semantically related In some cases you can use "Up-and-coming" instead an adjective phrase "On the up and up".

Up-and-coming adjective - Working hard to promote an enterprise.

On the up and up and up-and-coming are semantically related in promising topic. Sometimes you can use "On the up and up" instead the phrase "Up-and-coming" as an adjective or an adverb.