I would advise you not to get crazy, here. Before you start anything, take a magnifying glass and examine the stitches down past the throat where the brass used to fit and see how far they separate and where they join firmly.
That will tell you whether your repair will hold. If you judge that the threads are not so dried out as to fray further no matter what you do, or if you are thick headed and really want the repair ( remember that this is coming from the guy who once posted on making an Indian Brown Bess a viable gun, by the by) then re-read the posts above.
From this point on, you are a cobbler with little difference between you and somebody in the 19th century...except you got a whole lot more technology.
The throat of the pouch, where all the discoloring and fraying is, will either hold the spout or it won't. You probably won't be able to use the short bolt that appears to have gone through the leather throat to hold the spout on.
You should probably moisten the top of the throat and even it off with a knife sharp enough to shave with.
Moisten ( don't soak) the rest of the throat and insert the brass spout, leaving it until it dries. Use your fingers to encourage the fit but then leave it alone overnight. Gently, boy, gently.
Take the missus out to Starbucks and steal a couple of their coffee stirrers. Tomorrow, when you can see how and where the dried leather fits close to the brass spout, see if there is a hole where the end of the secured stitching meets the brass of the spout. If there's no gap, celebrate 'cause now you're cookin' with gas.
This is a two step fix. Use a drop or two of Krazy Glue Gel ( not liquid) to bind the seam where the thread is secure rather than try to re-stitch. If you only have to glue one or two stitches down, that is a good bet to stop the seam from spreading it's gap. Your chances are that the guy who made that pouch used a half caste in his stitching....sort of like the first knot in tying you shoes. If he did that, then the seam does not want to spread and the glue is not easily seen.
Now rough up the throat of the brass where it joins the throat of the pouch. Use those stolen stirrers to smooth over a thin layer of Krazy Glue on the brass and push it down into the throat of the bag. The glue is going to add to the integrity of whatever is left of the leather at the throat.
If you are not cursing me for a fool at this point, then you have fixed the damage but not yet fixed the cosmetic of the pouch.
Here's what I'd try...
Get some white string ( not hemp or jute, but more of a cotton postal string) and some tacky glue or Elmers. Paint the whole throat on the outside and let it sit for enough time for the glue to get tacky. Try to use enough to hold the string but not so much that it will run and bead up. Starting at the bottom of the throat, carefully wrap the string, in even, tight windings until you hit the brass lip. Hold it for a while and let it dry.
Once you know it is dry, you can stain the string if you want unless you admire the contrast of your handiwork.
Coat the windings again with anything that will seal and harden...even more glue will do. Cut the ends of the string.
Tah Dah....
Hope this helps and your lawyers don't know where I am if it doesn't
The Capgun Kid
AKA The Still River Cordwainer