But if I write about poetry bewildering people in a poetry competition can I get away with not writing what the poem is?
Fine lets spin it fantasy style, magic doesn't need to exist for someone to be showcased as good at it, when you the author likely don't have access to every magic system in the real world.
What are you trying to do, that is the key point here, I'll state it directly because there isn't enough to go off.
Are you asking how to write dialogue for a poetry focused character, to emphasise in a bard-like manner that they speak using that skill, or are you saying they have written some good works at some point in time and can get other characters to demonstrate and react; as with any skill, that they are advanced in their field.
If you are trying to ask 'can I claim something is impressive without presenting it' that falls into reader trust the same with any specialty.
Thats why a lot of novels people might read on some of the weaker websites have so many characters hyping up the main characters action because it turns out cultivation is slightly hard to do in the real world.
Thats why characters can focus on the process, the writing, the research or whatever skills they would need to show to the audience to understand they have that skill.
Either way for a character to be 'good' at something it still comes down to how others perceive the result of that task.