Yes. You can make either an ordinary Power of Attorney or an Enduring Power of Attorney.
An ordinary Power of Attorney is only in effect while you have capacity to make decisions. If you were to lose capacity the ordinary Power of Attorney appointment ceases. An ordinary Power of Attorney can be useful for a short term appointment, for example if you are going overseas for a month or two and wish to appoint an attorney to look after your legal and financial affairs while you are away. It is also useful if you want the attorney to act only in relation to certain one-off transactions, for example to sell (or buy) property on your behalf.
If you want to make sure your attorney can still operate if you lose capacity, you will need to make an Enduring Power of Attorney. An Enduring Power of Attorney will continue to have effect after you have lost your capacity to make decisions. This is important for everyone, but particularly for elderly people.
A Power of Attorney does not relate to decisions about your lifestyle, medical treatment or welfare. Where you live, what services you have and what health care you receive are decisions that can only be made by you, or if you lack capacity, by an appointed guardian.
The Power of Attorney role ceases when you die. The executor named in your Will then takes over the responsibility of administering your estate.