Assuming you mean Cordyline australis, check the trunk for signs of rot - oozing, with white, or orange gunk, or sunken, blackened areas. If none, then just wait - it may shoot new growth up the trunk or from the base or both, and when it does, cut back to that point. You may have to wait a good while before seeing any growth, perhaps as late as June. If you have rotted areas, cut down beyond those now.

Exactly the same advice as Bamboo has said applies for the Mediterranean Palm Tree (Chamaerops humilis). I have never, personally, seen it regrow if the main stem has rotted, though their is a first for everthing.

Never heard that before, Kildermorie - as far as I know, once the growing tip's been killed at the top of any true palm, its a goner, won't regrow from lower down - except for Cordyline. Suppose its worth a try, but my book says it won't work...

Chamaerops humilis frequently produces new shoots from the base, though occasional specimens seem determined to have single trunks. The trunk and crown of Trachycarpus species resemble Chamaerops, and they don't sprout from the base.