A few more photos would help. It's not clear to me what the problem is. Jon says the jaws look worn, and then covers them with tape! Could be the jaw faces have been abused, or screws & teeth mangled by excessive tightening, or perhaps the wrong jaws have been fitted. (Not all pre-loved lathe owners are geniuses!)
Reassuringly expensive products are not immune to mistakes or being thrashed. Assuming the chuck body and screws are OK, possible to buy replacement jaws for Pratt Bernerd chucks, though unfortunately the company is a Price on Application operation. Whether or not spare jaws can be found for an old chuck is another question.
Assuming the worst and a replacement is necessary, ask if buying a 'decent' chuck is worth the money. 'Decent' is deeply suspect as an engineering specification. Professionals look for 'value for money' and 'fit for purpose' rather than 'decent,' 'good' or 'quality'. Those words waste money galore because best is the enemy of good enough.
Expensive tools tend to save time rather than provide marvellous extra capabilities. And they usually resist wear and tear longer in busy workshops. Being smooth in operation makes centring work in a 4-jaw that much faster – but not more accurate, or with a stronger grip! Down to the operator to decide if smooth operation and long-life are worth spending money on. Time wasted by second-class tooling is irrelevant to the experimental moderate precision work I do. Same tools would be a major problem if I machined for a living: time is money.
Psychology plays a major part in amateur workshops. Pays to consider your mindset. My outlook is utilitarian: tools need only be good enough to get the job done. Others see it different, because not only is pleasure to be had from owning and handling 'good' tools, but some find imperfect tools downright frustrating. As hobbies are to be enjoyed, strong feelings may be a must scratch itch, even if absolutely unnecessary to the job. Another manifestation: clean tidy workshops versus stuff everywhere. A shortcoming of the clean tidy approach is keeping workshops neat often become more important than making anything! As opposed to untidy workshops were nothing is made because the lathe is under a boat.
Buying tools, I advise being honest about why it's wanted. Don't buy a mini-lathe if the goal is to put the club's boastful Myford Connoisseur owner in his place. Best way to deal with swankers is to install a Dean Grace & Smith in a purpose built air-conditioned workshop, with a long story about the cost of running 3-phase across your land. But bear in mind a mini-lathe is a better choice than a big DSG for most hobby purposes.
Point is, a new Far Eastern 4-jaw bought from a reputable source will do the job. Order today, delivery next week. Don't do it if your gut rejects the idea!
Dave