Depends what you mean by Palm tree - most palms won't like that treatment at all, but if yours is a Cordyline, it might respond by sending out new growth from the base - but don't do it at this time of year, wait till spring. If it is a Cordyline, you could just cut it down by half or two thirds, and it might then branch from the remaining trunk as well.

bamboo i have a cordyline and it is about 23 ft tall well up above bedroom windows and this year has put out new shoot about 1 mitre from ground and wondered if i should cut the whole tree down or cut to new shoot as i dont know how tall it is going to grow to and also dont know how far it throws roots out

Walto, you could cut it down next year to that new shoot, but its always a risk, and certainly, if the plant doesn't mind too much, it will probably throw up new shoots all round the base - which you might not want. On the other hand, if you're concerned about its root spread (though its nothing like, say, a broadleaf tree, laburnum, etc.) might be wise to chop it back anyway. But as I say, I wouldn't normally recommend it unless the topgrowth is damaged and the main stem is showing signs of damage too... Alternatively, if its outgrown its space and is blocking light, no reason why you shouldn't just get rid of it altogether and have a rethink about the area.