What is the meaning of ことに当たるように in this example (there is already a post of にあたって/にあたり, but I can't understand)?
It's a fixed phrase:
(Translation: take charge of / engage in some work: "The whole company was involved in the ceremony.")
(The linked entry also has a second definition, but it's classical usage. Forget it.)
ように that ends a sentence should be interpreted as formal command.
From now on, you should cooperate with Tom to handle it.
You may be confused because both こと(①-3) and 当たる(5-㋐) are used here in their original meanings, rather than as function words. The best practice is writing this こと in other than hiragana, but sometimes they do this way. Nevertheless, you'll know the こと isn't a nominalizer but a standalone noun because 協力して can't connect to it in this form.