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?
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.