Personally, I'd just go with more goblins
For many players LMOP is one of their first experiences of DnD – if that’s not you, and this answer feels too simplistic, feel free to ignore it.
I really like your idea of having some other creatures moving in the goblin’s territory – it’s touches like that from a GM that help a world feel real and active rather than static, to players.
There are plenty of creatures from the MM that you could use for this purpose, all of which could be fun for your players, however, I’m not sure there’s much benefit in overcomplicating things. I think one of your best options is probably just introducing more goblins to the mix.
So, you’re players have struck an uncomfortable bargain with Yeemik and killed Klarg. Klarg was the Cragmaw tribe’s appointed leader at the Hideout, so what happens when the Cragmaw goblins, from elsewhere, find out he’s been killed?
Maybe the next loyal Cragmaw patrol that stops in gets wind of Yeemik’s betrayal and decides he needs to be removed from office? Or, perhaps that patrol thinks Klarg’s death has created a power vacuum that they’re well-placed to take advantage of – using Yeemik’s actions merely as an excuse for their own ambitions. If you preferred, you could even create an entirely separate tribe of goblins looking to move in on Cragmaw territory.
Advantages of this approach:
- All the stat blocks you need are already in the LMOP campaign book, including hobgoblins and bugbears.
- We already know it's alocation well-suited to goblin occupation.
- It doesn’t dramatically change the campaign setting in an on-going way.
- If you do have access to MM or VGTM you can introduce a more diverse range of greenskins (as an example, the Gobin Boss’s ability to redirect attacks can be hilarious in goblin-on-goblin violence)
- Green on green violence is commonplace: 'They crave power and regularly abuse whatever authority they obtain.' 'Their larger cousins, hobgoblins and bugbears, like to bully goblins into submission.' 'Goblins are ruled by the strongest or smartest among them [...] Goblin bosses are easily ousted, and many goblin tribes are taken over by hobgoblin warlords or bugbear chiefs.'
Ultimately, you should go with what feels right to you, both narratively and effort-wise.
If that’s not more goblins, but you have access to limited resources, there are other factions already present in LMOP. You could probably come up with a narrative reason for moving any of them into Cragmaw territory, if you wanted to, including Orcs, a Necromancer, Redbrands and dragon worshipping cultists.