That's a tough clue, since like half the remaining words seem to fit; we'll have to look for overlap with Barracks, where we've got two outstanding, but presumably JR is trying to get us across the line this round, so only one of the Barracks clues should overlap (at least in a way that was clear to JR), otherwise a 3-clue would leave us one short, with nothing to go on for the bonus guess.
We can probably rule out Ham, what with the Veal connection.
Both Horse and Yard make sense to me as dual Barracks / Butchering words. Not sure which is better, or if both are correct and JR didn't see it.
I like Theater as the Barracks word with no Butchering crossover, despite the potential for it being Blue.
An Octopus is something you'd butcher. A Pie may require Butchering to prepare. Neither word overlaps with Barracks or Beauty.
Shop works with Butchering, but also has a severe chance of being blue; I wonder if "Butchering" instead of just "Butcher" was meant to steer us away from it.
So... tentatively for Theater, Octopus, Pie, and then one of Yard of Horse.
The connection between Ham and Butchering is beyond obvious, but, while I hesitate to do Blue's work for them, what of the remaining words could make more sense for Veal than "Ham"? Pus they got a four-word clue, meaning one of the Veal words they were contemplating was correct, and they had essentially declared they would go for Ham next. If Ham was Red Fenn would have surely attempted to direct them away from it, since it'd be better to win in two rounds than attempt to win in one with a very high chance of instead inadvertently giving us a word.
I reckon that JR is cognizant of all this, and clued Butchering with the assumption we'd ignore Ham.