press on

present singular third person presses on · participle present pressing on · participle past pressed on · past pressed on

1. idiomaticTo persist, to continue to advance.

   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.

   2017 July 23, Brandon Nowalk, “The great game begins with a bang on Game Of Thrones (newbies)”, in The Onion AV Club, archived from the original on 26 Jul 2017

   1 more example

   British Railways are, however, pressing on with the introduction of standard equipment, and in this, the fourth year of unified working, standard locomotives and rolling stock will be coming into service in considerable numbers.

   1951 April, D. S. Barrie, “British Railways: A Survey, 1948-1950”, in Railway Magazine, number 600, page 225

   Synonyms: press ahead