Not clothing, just leather. Leather scraps, if it’s cheaper, and also some basic leatherworking tools. Where would I find this sort of thing? Craft shops?
Most craft store chains (Michael’s, A. C. Moore) have exactly what you’re looking for.
When I was making holsters for my black powder revolvers (and a shoulder rig for my then-g/f’s Ruger Mk.II) I bought my leather and tools at a chain called Tandy Leather.
Tandy Leather is good, they’ve got a pretty extensive website. I am a leatherworker as a side job, I make handcrafted leather dog stuff. I buy all my leather–whole hides, garment leather, scraps, etc–from Oregon Leather Supply, which as you might guess deals entirely in leather, leatherworking tools, and stuff made out of leather.
As far as craft stores, I think it depends on what you’re looking for. There are no general craft shops in my area that have good quality leather or quality tools. Sometimes they’ll have suede-like lacing and light garment leather kits for making doll clothes and suchlike, but not anything terribly sturdy like latigo, harness leather, upholstery leather and so on, and certainly not whole or half hides.
People gotta keep in mind that FRM is in Perth, Western Australia. Not Washington (or whatever WA stands for with your crazy-ass state abbreviations 
), so any suggestions need to be either online and allow shipping to AU, or based in Australia.
Bigger chain craft shops like Spotlight are always a good place to start, if you’ve got one nearby. That said, however, recently when I’ve been in Spotlight they’ve been big on things like leather thongs for beading, but not actual leather. With the recent explosion of that terrible scrapbooking cult in Australia as well, any scrapbooking stores are going to be worth checking out. I’m sure I saw some harridan on TV doing a scrapbook with leather pockets one day. Leathergoods stores will often sell offcuts of leather as well, but I don’t know what your prices are going to be like. Most markets like Paddy’s Markets will have a leathergoods seller or two in there. Even if they can’t sell you any, they may be able to give you some details about where to get the offcuts and scraps you want.
If you just need some smaller pieces you can sometimes buy used leather purses at Goodwill or Salvation Army for a few bucks. Some are in excellent condition and are made with thick, very high quality leather that is as good or better than anything you could buy in craft type leather store.
Perhaps there’s a source here?
I’m making a Mantis costume and need leather straps to make the rig he’s wearing, some of which are fairly long. Spotlight doesn’t have that. I haven’t checked Lincraft but I bet it doesn’t either. I’ll go have a look at the store from Johnny’s link some time, thanks.
For costume purposes, I’ve had good luck buying lots of leather scrap on eBay. You might also want to consider black vinyl if you don’t want to shell out for all the leatherworking tools; good black vinyl will look like leather enough for a costume, and is less expensive and easier to work with. Most fabric stores will have it.
Used purse straps would work.
Purse straps? You mean… buy identical purses and cut up the straps? Or is there some sort of store where you can just buy purse straps on their own?
(I only own one purse and I’m not cutting it up because I need it.)
You could also buy a few cheap leather belts (men’s XL length) at WALMART and split them into several straps, or get belts from Goodwill or Salvation Army for a dollar or two each and do the same.
Saddlery or tack repair shops will often sell leather scraps. Actually, stirrup leathers would be the right length for what you need, but they’re rather pricey for a costume. I think the leather belts idea is a good one.
No Wally World here in Australia, either. (Can’t say as I miss it, though.)
But that’s a point, try Kmart or Target or Big W for cheap leather belts, if you just need straps. By the time you buy leather and tools, it would probably work out just as well.
Alternately, you’re in Perth…have you thought about sheepskins? Most of the touristy places have them, that might do for a lot of leather. They’re cheap as here in Sydney.
Cheers,
G
When my brother did leatherworking it was always tiny pieces; he got scraps from the shoe repair place.
If there’s a shoe repair place near you, you can ask where do they get it 
Uh, right. I was only trying to be helpful in giving an example of where I buy my leather, so she could look for a similiar type of business near her. Tandy Leather is, in fact, online although I don’t know if they ship to Oz or not.