how to cheer up or show support in german?
in a competitive scenario or situation

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Hello,

actually, to cheer sb. means: jemanden anfeuern: Die Zuschauer feuerten die Fußballmannschaft mit lauten Jubelrufen an.

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Do you mean at a soccer match in the stadion? You can say:

"Klasse! Toll! Weiter so! Vorwärts! Schneller! Tor!"

There may be more examples.

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I can't help with the German, I'm afraid, but may I make a comment about your question? The word you want is 'cheer' , not than 'cheer up'.  
for example : 'The crowd cheers the players'. 'Cheer up'  means to make a sad person feel happier.  And good luck with finding your German phrase.