Some commentary on the issue.
It seems that conventionally you don't have the right to have a legal representative but you can request it.
Who is legally entitled to attend?
Both workers and employees have the legal right to be accompanied to a disciplinary or grievance hearing. However, in accordance with section 10 of the Employment Relations Act 1999 those rights are limited to being either a trade union representative or a colleague. The right for the individual to be accompanied by either of these two is absolute and regardless of whether their choice is considered to be inappropriate.
Are they entitled to bring a lawyer?
It is not unusual for an individual to ask to attend or be legally represented at a disciplinary or grievance hearing by a lawyer. However, unless there is a contractual agreement there is no legal rights over and above attending with a colleague or trade union representative.
That being said, in limited circumstances the individual may be able to establish a right to legal representation where a failure to allow may impeach on a fair trial, but this is extremely rare and relates to proceedings where an organisation could have the power to prevent someone from practising their profession.
https://amicahr.co.uk/can-i-bring-a-lawyer-employee-rights-at-disciplinary-hearings/
I should think that if SP were to request it, NHS Fife would be extraordinarily unwise to refuse. That said, it's NHS Fife so…