well the new shoot is the importent part .if you cut the old leaves of that will help put the energy into the green stem and protect them next year.a lot of semi hardy plants do aclymatise to our weather after about 5 years but not all of them.

If you mean Phoenix canariensis, you've been very lucky it survived the winter if you kept it outside. Noseypotter's right, all that counts is you have new growth coming from right where it should be, the growing tip. Remove all dead leaves as close to the "trunk" as possible.

its normaly the other way round almost isnt it bamboo ?