I already think I know how to say this but looking for a more definitive answer.
Tempus Edax Rerum is my thought?
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Tempus edāx rērum doesn't literally mean "time the devourer". Edāx literally means "gluttonous"; it comes from the verb edō "to eat". But in English it's much more natural to use the noun "devourer", since we don't generally form adjectives from nouns. The general meaning is the same: Time is devouring everything. (You could also drop off the rērum, which just means "of things".)
This phrase comes from Ovid's Metamorphoses, book 15:
flet quoque, ut in speculo rugas adspexit aniles,
Tyndaris et secum, cur sit bis rapta, requirit.
tempus edax rerum, tuque, invidiosa vetustas,
omnia destruitis vitiataque dentibus aevi
paulatim lenta consumitis omnia morte!
And the daughter of Tyndaris [i.e. Helen] also weeps, when she sees in the mirror the wrinkles of an old woman, and asks herself why she has been forcefully taken away twice [i.e. once by Paris, and now by aging]. Time, gluttonous for things, and you, envious old age, you destroy everything, ruined by the teeth of eternity, slowly, little by little, you despoil all things with death!
(On a side note, the poets liked the word edāx. Ovid also applied it to fire in M.9, and nature and old age elsewhere in M.15.)
I started writing this before the other answer was posted, but I was nearly finished, so I am not going to let my time be devoured after all the work I put in, so I'm still posting it! :)
I would tend to disagree with your translation, for the main reason that edax is an adjective, so your translation reads "time devouring of affairs," which doesn't quite capture the idea for which you are going. So here is my suggestion:
Tempus Devorator = Time the Devourer/Glutton
I especially like the word devorator because of the "glutton" meaning in this context because it implies that time keeps devouring and simply can't help itself. There are also words that can be substituted in for each other to find the perfect combination. Important to note is that one must match the gender of the word for time with that of the word for devourer. If time is masculine, then use the ending -or, if it is feminine, -rix. Tempus is technically neuter, but is personified here, so an ending like -rum doesn't work (as it generally means a thing, not a person). I therefore just use the masculine with a neuter time. Here are the other options
Like I mentioned at the beginning, after I saw the other answer, I agree that edax could potentially be used in that sense. These are just some other options.