When you start the car, there is a squealing sound coming from the front of her, it maybe a pulley bearing, it doesn't stay squealing for a long time.

 

Loose belt? Have you checked?

Harmonic balancer delaminating? Fairly common.

Cheers
DD

 

Probably better if you post in the forum for your car, which from the year is one of the X300 series built 1994-1997. Look in the Modern Jaguars section. This forum is for the last of the old style XJs built of aluminium and which are totally different to your car. However, Doug's advice is correct, the squealing is because after a start, the alternator is recharging the battery. This puts more load on the drive belt, and if it's loose, makes it squeal.