You need a horse with high enough skills in the main skill for the chosen comp. Generally speaking they need a minimum of 6500 to see rosette comps. With the exception of very few comps they are also usually reserved for horses with over 20 wins.

If you get 20 wins with Geyser you'll be able to enter one rosette comp most days with them. If they had 20 wins now they'd do well in a trot rosette comp today