Harry Lauders Walking stick bush aka Corylus avellana contorta or Corkscrew Hazel does have this annoying habit of throwing up straight suckers from the root. They will grow more quickly than the twisted branches and spoil the whole effect. They need to be removed regularly and I find the best way is to pull them downwards and tear them off - if cut off they quickly resprout .

I know of no way to prevent the plant producing suckers except perhaps avoiding cultivation around the roots as with some plants even slight damage can trigger the growth of suckers.