Yes, first thing to check is the styli (needle) and the cartridge (the fitting which holds the "needle") these are usually the first things to wear on a turntable, although the styli is most likely to be the problem

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You can check this easily enough before buying replacements, by simply swapping it over with the one on your other turntable. If it cures the problem then you know which bit to buy.
Try replacing the styli first, then if that fails swap over the cartridge as well.