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We tried feliway, too hard to know how much difference it made. But worth giving it a go.
We got Nico (tabby) when Fred (now departed) was quite old. Fred attacked Nico at first. These two never really became friends but Fred did learn to tolerate Nico.
Then Fred died and we got Stevie (black and white muppet featured above). We assumed Nico would be fine with Stevie as Nico had never been an "only cat" like Fred had been. Turned out not to be the case. Nico bullied Stevie and we had to separate them at first. Within a month most of the violence stopped though.
Now they get on well with the occasional play fight.
Mine weren't best friends to begin with but they get on fine now.
Hopefully yours will settle in a month or so.