Definition of "push on"

push on

verb
third-person singular simple present pushes on, present participle pushing on, simple past and past participle pushed on
1. (idiomatic) To persist, persevere.
  Quotations
  The rider, to whom the paths of these wilds seemed intimately known, pushed on at a rapid pace, managing, with much dexterity, to chuse the safest route, […]
  1815 February 24, [Walter Scott], chapter II, in Guy Mannering; or, The Astrologer. […], volume II, Edinburgh: […] James Ballantyne and Co. for Longman, Hurst, Rees, Orme, and Brown, […]; and Archibald Constable and Co., […], page 30
  The object of the builders was to push on to Uganda as quickly as possible; one result was that Kenya was "discovered" on the way.
  1950 April, Timothy H. Cobb, “The Kenya-Uganda Railway”, in Railway Magazine, page 262
2. Used other than figuratively or idiomatically: see push,‎ on.