new chain

hi having chain trouble fitted a new chain to my bike a KMC X8-93 to replace a KMC Z51 but new chain slips in high gears under load I have fitted a new rear derailleur and this works fine when I use old chain it works ok . could this be that the sprocket has worn and old chain is more suited to it. bike is a Dawes Tamarack dx with Shimano chain ring and 8 speed cassette :?:
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But I'd still fit a new cassette