In Star Trek Discovery S1:E3 - Context is for Kings, we see Lorca's collection of extraordinary items, including a Tribble.
Now the trouble with Tribbles is that they multiply.
My question is: Why does Lorca only have one Tribble?
How does he have only one?
We don't know for sure cause the show hasn't said (as of 11-7-17). But to pull a quote from TOS.
Dr. McCoy: [enters after Kirk gets covered with tribbles] Jim! I think I've got it. All we have to do is quit feeding them. We quit feeding them, they stop breeding!
Capt. Kirk: Now he tells me.
He either knows enough not to feed it (probably the explanation), or there's some less canonical explanation like it's a male (are there males?), it's fixed, or it's stunned or dead.
I like the not feeding it option best and I hope they go with that.