press on

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press on (third-person singular simple present presses on, present participle pressing on, simple past and past participle pressed on)

1. (idiomatic) to persist, continue to advance
   • 2017 July 23, Brandon Nowalk, “The great game begins with a bang on Game Of Thrones (newbies)”, in The Onion AV Club‎:

     And now she has the real dilemma: press on to King’s Landing, where I have no doubt she could get as close to killing Cersei as anyone else, or double back to Winterfell to reunite with her family.

• press ahead

• Persons, Posners, persons, spreons