It will be the ceramic cartridges. They don't last very long.
If you know the make, you can buy replacements to fit, if not you can take out the old ones and see if a spares shop has one suitable.
In the centre of the handles is probably a plastic cap, covering a screw to take off the levers, which exposes a large brass nut to unscrew the cartridges with a (preferably ring) spanner.
Turn the water off first, put the plugs in and cover the sink with an old towel to catch the bits you drop.
You'll need to access the ceramic inserts (one hot, one cold) and replace them......they are probably screwed in.
You'll need the make of the tap as there are many different types!
Try TapSpares.co.uk for help.
John
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