Then your LA (assuming in England) are doing it wrong.
You only 'apply' for a tree with an existing tpo or covered by an area tpo.
Any tree over 3" dbh in a CA needs only to be given the chance (6 weeks) to be protected.
Anything else you can do as you please....
Unprotected trees in CA: (from planning portal)
Notification of proposed works to trees in conservation areas
In conservation areas, notice is required for works to trees that have a trunk diameter of more than 75mm when measured at 1.5m from ground level (or more than 100mm if reducing the number of trees to benefit the growth of other trees).
You have to give your local planning authority six weeks’ notice before carrying out work on trees which are located in a conservation area but are not yet the subject of a tree preservation order. This gives the authority an opportunity to consider whether an order should be made to protect the trees.
When to use this form
You will normally need to contact your local planning authority (LPA) before any work can be carried out on protected trees. The LPA is usually the council to which you pay your Council Tax, but where the tree(s) are in the Broads Authority area or a National Park you should consult the relevant Authority.
Protected trees include those covered by a tree preservation order (TPO) or those which grow in a conservation area. You will need to contact the LPA even if you wish to prune branches overhanging from a neighbour’s protected tree. You should send one copy of the completed form to your LPA.
• TPOs - If you wish to carry out work to trees protected by a TPO you must apply using this form. Your application, and any subsequent appeal, will be decided on the basis of the information you provide now, so it is worth getting it right at the start
• Conservation areas - You must give six weeks' notice before carrying out work to trees in a conservation area that are not protected by a TPO. You may use this form for this purpose or you may send a letter or email, which must still include the information required by the form. This gives the LPA an opportunity to consider whether a TPO should be made to protect the tree(s)