Hedgerows Ireland is currently exploring the archives of the Department of Agriculture to uncover the origins of the current ineffectual regulations around hedgerow removal. As things stand today, it is perfectly legitimate to remove up to half a kilometre of hedgerow without requesting expert advice or permission. This could involve grubbing up an ancient townland boundary hedgerow, possibly hundreds of years old, or a hedge with rare or threatened species, bat roosts, owl hunting corridors etc. It's entirely up to you as owner to decide if you need to ask for an assessment by the Department.
Some insight into the attitude of Department officials toward heritage hedgerows, for example, can be found in this extract from documents from 2011 obtained under FOI (Freedom of Information.)
In this document DAFF is the Dept of Agriculture Fisheries and Food and DEHLG is the Dept of the Environment, Heritage and Local Government.