Noise from water pump

I recorded a Youtube of the noise. It is the slightly higher pitched screetching noise you will hear. It appears loudest in the vacinity of the water pump. If I replace the pump, is this likely to go away? I hear this after starting the engine from cold, later it goes away. Is there anything else I need to order in addition to the pump? I read people replace a p-gasket, any idea what the part number is? I have a 300tdi.

https://www.youtube.com/watch?v=RPD4Bv4JAlQ

Regards.Fred

Have you tried adjusting your fan belt??

the video if private....