I don't do skating competitions but I do play a fair bit of tennis. Most of my tennis is practice rather than matches and when I started playing for points I always found I played well below the level I played in practice and felt very demoralised. Initially I just tried to practice even harder so correct faults that emerged in matches. This worked up to a point - the better your technique the more confident you are and this confidence will be harder to dent under pressure - but ultimately I realised that the biggest issue was mental. I have talked about this with a lot of players and coaches and the consensus seems to be that the way to get good at matchplay is to play a lot of matches. Eventually your subconscious realises you CAN make shots under pressure and you relax. You also learn to focus (in a relaxed way) under pressure. I think you have to at some point start enjoying the process, relishing the challenge. It's remakably hard to do and you realise how good the professionals are at concentrating 100% point after point, shutting out the outside world.
Sorry, all this is rather obvious and I cannot offer any magic, but for me just persevering has worked. Also I try to take positives out of every match - maybe I lost but played well, or maybe I played badly but even so I stuck to my gameplan and the execution was lacking because my timing was just a bit off that day. Of course improving your skating is going to help too - if your technique is solid and your spins or jumps NEVER go wrong in practice then you may start to believe they won't go wrong in competition either. Perhaps too you could have your coach simulate competitions by watching you run your program and marking it, not allowing you to restart if you fall. I still get nervous playing matches, and hate it when I play poorly, but I have started to accept that this is natural and that the situation can be improved over time, and that it is VERY COMMON for sports people to get nervous and underperform. There may be some outliers who perform better under pressure, for most of us mere mortals I think it is the opposite.