Translation:Please do not play tennis here.
It's a more casual form of する, though they are not always interchangeable. The link above gives good examples of when to use each.
To say "please don't do X" in Japanese, you use the negative -te form of the verb + kudasai. The negative -te form of やる (yaru, no kanji necessary) is やらないで (yaranaide).
You would use やらなくて (yaranakute) if you were asking permission to not do something.
Yaranakute mo ii desu ka?
Is it okay if I don't do it?
The drop down "hint" for "やらないで" says only "do not"! It gives no useful info. It is in fact misleading, because I (and many others I'm sure) could only get "Please do not tennis here" out of the sentence, where tennis is a noun, not a verb. Then the 'surprise' correct answer. ".. play tennis.....". I'd guessed the missing verb was "play", but no thanks at all to duo! I have told duo it would be nice if duo would amend the drop down "hint" for "やらないで" to say "do not do, play, etc", or something of the sort. This is a new verb to me.
テニスをしないで would be correct. A native speaker confirms that either is correct above: https://forum.duolingo.com/comment/24191635?comment_id=25758150
やります tends to sound more colloquial than します, but otherwise they are pretty interchangeable. This article at KawaKawa Learning Studio goes more in depth about the differences: https://kawakawalearningstudio.com/all/different-ways-of-using-%E3%82%84%E3%82%8B-yaru-and-%E3%81%99%E3%82%8B-suru/#:~:text=In%20general%2C%20in%20situations%20where,more%20useful%20than%20%E3%82%84%E3%82%8B%20yaru.