I believe it is only appropriate when the speaker is an elder or at least about the same age as Thrakhath. The new manager is "new" because this person was not a manager when birth, but has recently assumed this position. But Thrakhath had been a Prince since birth.Going by earlier dates, Thrakhath had only become the crown prince at the most a year prior to Firekka, due to his father's execution; his elevation was brand new.
I do not think that Thrakhath was ever shown as being respected by anyone, and by referring to him as 'young' prince or 'young' crown prince is factually correct, in comparison to Gilkarg, and would immediately bring to mind his predecessor who was much more accomplished than Thrakhath, as well as the over-reaction of the emperor. Ralgha could not have been the only Kilrathi who could see the way the Kirankas were mismanaging the empire and the use of 'young' to describe Thrakhath is the perfect way to show social disrespect without reprisal because the statement is technically correct. If we saw other nobility in the novel, they would probably use the same term, as the breakdown of social decorum among the highest levels of the imperial court started years before with the lack of discipline of the Kirankas in Action Stations.
The same could be seen in the present day any time someone is introduced as the 'new' manager; they will still be the 'new' manager until another is hired, but the tone in which they are referred to is where the insult would come in.
Well... if Thrakhath can be objectively described as young at this time, the side note could be that Kilrathi's twenties is not considered old. Combining the multiple depictions of the book, Ralgha did not look like a youth, so it's not like he would be much younger than Thrakhath， thus he was not likely to be 15 years old.
In short, I think it is the following.
1. if Ralgha subjectively evaluated Thrakhath as young, then it was appropriate only if Thrakhath was not obviously elder than him.
2. If Thrakhath was objectively evaluated as young for the age, then Ralgha didn't look like a younger Kilrathi.