A new chain (OP has checked it with a 'chain checker') does not wear an old cassette. But 6000 miles with one new chain means it will be well worn. You need to test this by getting out, large ring and middle sprocket and then put some power down up a gentle hill, anticipating a slip (you have not described this symptom so far). If it slips (try it on several of the sprockets) then replace both cassette and chain. If it doesn't, ride on, till it does.
In the future, you may find it economic to change the chain every 1500 miles and thus minimise the wear on an expensive 11sp cassette. You have got good distance out of the current one.