To Perform
To Play
transitive verb
If 演 is performance then the verb version of this would be to perform.
The reading looks weird, but it's actually just the reading you learned with the kanji.
「演ずる」は「演じる」の、よりフォーマルな表現です。
"Enzuru" is a more formal expression for "enjiru."
尻尾で喜びを示す犬の役を演ずるのがどんなに大変なことか、あなたは分かってらっしゃらないようですね。
You seem to not understand how difficult it is to play the role of a dog that expresses joy with its tail.
この度、私は、次のYoutubeビデオで、アメリカ大統領という大役を演ずることになりました。
I am excited to announce that I have been chosen to play the pivotal role of the United States President in our next YouTube video.