go on to

go on to (something)

To progress to something better or more prominent. Quite a few soap actors have gone on to win or be nominated for Oscars, actually. After being an intern there for three years, I'm ready to go on to bigger and better things. Did that famous child actor go on to do much as an adult?
See also: go, on
Farlex Dictionary of Idioms.

go on to something

to advance to something or to doing something. After a few years she went on to even greater heights. Larry went on to found his own company.
See also: go, on
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.
See also:
  • go on to (something)
  • soap up
  • soap down
  • have the (brass) face to (do something)
  • have the face to
  • have the neck to do something
  • have the (brass) neck to (do something)
  • give (one) (the) clearance to (do something)
  • what do you want to bet (that)
  • speak of
References in classic literature
As to which quantity there was a perpetual fight going on between the master and his form--the latter insisting, and enforcing by passive resistance, that it was the prescribed quantity of Homer for a shell lesson; the former, that there was no fixed quantity, but that they must always be ready to go on to fifty or sixty lines if there were time within the hour.
Tom Browns Schooldays
Through Blyth, we were able to demonstrate to the watching world that the technology worked, and we've been able to use our experience and learning to go on to develop a further 1.5GW of wind capacity off the UK coast.
Two of first turbines in region to be dismantled