Definition of "step up"

step up¹

verb
third-person singular simple present steps up, present participle stepping up, simple past and past participle stepped up
1. (transitive, idiomatic) To increase, augment, or advance, especially by one or more steps.
  Quotations
  United were made to pay for letting an eight-point lead as little as five weeks ago slip and, despite their final-day efforts, they will look back on a season where, when they needed to step up, they fell flat.
  2012 May 13, Alistair Magowan, “Sunderland 0-1 Man Utd”, in BBC Sport‎

step up²

verb
third-person singular simple present steps up, present participle stepping up, simple past and past participle stepped up
1. (intransitive, idiomatic) To assume or take responsibility.
  Quotations
  The Gunners continued to press after the break but it was Leeds who broke the deadlock in the 54th minute. There was no doubt about the penalty either, with Denilson clumsily fouling Gradel and Snodgrass stepping up to find the bottom corner of the net.
  2011 January 8, Chris Bevan, “Arsenal 1 - 1 Leeds”, in BBC‎