The best way to eliminate wordiness is the following:
The audience gave the guest speaker a standing ovation.
Wordiness is the use of more words than necessary to express an idea. The phrase "to give a standing ovation" already comprises the ideas of "rose up" and "applauded". Thus, they are not necessary in the sentence. Replacing those words with the words "gave the guest speaker a standing ovation" is the right way to eliminate wordiness in that sentence.