Difficult - this shrub is often very reluctant to produce new growth from old wood, so the usual method of keeping these from getting leggy with age is to prune lightly but regularly, that is, yearly or every other year. If you really don't like how it looks, you could try cutting it back to see what happens, but don't attempt it until Spring is well and truly here.

Hi, I would have thought that as a palm, it would naturally get leggy, forming a trunk of 30 to 50 ft,
however, if you mean the shrub, CarpentEria, then I would agree With Bamboo, Derek.

I assumed it was Carpenteria californica that was being asked about, Derek... I don't think I know a palm with a similar name anyway.

Hi Bamboo, I was a bit undecided, as the question said Carpentaria, but also called it a shrub.
Carpentaria, is a genus of 1 species, Carpentaria acuminata, native to Queensland Australia, whilst Carpenteria, also a genus of 1 species, as you say, C californica, as the name implies, native to California U S A
but 1 is a palm, the other a bush, it isn't very often you get plant names so similar, but will agree, it is more likely that the question refers to the shrub and not the palm, Derek.

Derekm: Well, luckily, I'd never heard of Carpentaria acuminata, lol! Thanks for the info, always interested to hear something I don't know, shall look that one up out of sheer curiosity. I guess if the question is about the palm rather than the shrub, then we'll be advised.

UPDATE - I just had a look, and its that palm I've seen in Florida, never knew what it was called. Never seen one here though.

Hi Bamboo, no I don't suppose anyone will grow it in UK,it being frost tender, and that size, whereas the shrub is frost hardy and can be protected, Derek.
Ps glad to be of service Bamboo, Derek.

Yea, thanks Derek! Question is, will I remember that name though...

LOL, Derek