It's not a Yucca, but a distant relative in the same family. It is
Cordyline australis aka 'Cabbage Tree', 'Cabbage Palm', 'Torbay Palm'
etc. etc. It's not a palm nor is it remotely related to the palms, but
folks will insist on using that name. The single 'trunk' topped with a
head of leaves is the juvenile phase, which usually lasts for 5 - 7
years with the older leaves naturally dying away as the 'trunk'
develops. In time, a large, terminal panicle of small, greyish white,
pinkish white or yellow tinged white flowers is produced, often
followed by a mass of rather attractive, pea-sized, white berries.
These last for several months or at least until the jackdaws discover
them. No more leaves will be produced by that crown since it has
fulfilled its purpose and produced a flower spike. The old foliage
eventually dies away since leaves can't last forever.

However not all is lost. Several new shoots form at the base of the
flower spike as it develops. These grow and extend, forming branches
with new crowns that flower after 2+ years when they have attained
sufficient maturity. In time you end up with a rather splendid
branching tree regularly producing masses of flowers. That is until we
have a truly cold winter with prolonged, penetrating frosts, which kill
all of the top growth. Then, the thick, fleshy, subterranean
rootstock produces lots of young shoots part-way through the following
summer. In time these develop into a thicket of 'trunks' if allowed to
grow naturally and the process starts all over again. Yours has already
produced one basal shoot and this will flower eventually, giving you a
twin trunked tree that could look rather impressive.

Your plant is in the transitional stage following its first flowering.
All of the leaves on the current flowered 'trunk' will die away, but
will be replaced with more on the new branches about to form. Hot, dry
weather accelerates the death of older leaves, which is why it appears
that a lot of them are dying away suddenly. If you want the leaves to
last longer, water the plant well in summer and feed it regularly. All
Cordylines grow best in rich, moist, but well-drained soils and can
struggle when conditions are parched and starved. I suspect that this
long dry summer had far more to do with the rapid yellowing of older
leaves than the fire.