Recommended to try in similar climates to Northern Ireland

Trachycarpus fortunei (Chusan Palm)
Hardy in most parts of the U.K. and Ireland
Reputed to be able to survive as low as -18°C
T. wagnerianus - smaller leaves, more wind-resistant
There are other hardy species and some new discoveries
(Visit The Palm Centre)

Cordyline indivisa (Mountain nei nei)
Pictured here at Mount Stewart Gardens, Newtownards
At least as hardy as the more common C. australis
A young plant in my own garden, survived -10°/-11°C
while C.australis was killed to the ground

Musa basjoo (Hardy Banana)
A hardy banana? Well, root hardy at least
With protection the trunk can survive severe frosts
Otherwise will resprout from ground level
You may even get a bunch of mini bananas

Yucca glosiosa tricolor (in front M. Basjoo)
Survives rain, wind & severe frost - very tough

Beschornaria yuccoides
A softer-leaved, yucca-like plant
Dramatic coral red flower spikes in early summer
First flowering tends to produce larger flower spikes
(as in this picture)
Expect some damage from temperatures below -5°C
Can survive -10°C (but not much more I suspect)

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Chamaerops humilis (European Fan Palm)
Pictured at Mount Stewart Gardens - arborescent form
Not as hardy as Trachycarpus but more wind resistant
Can stand -10°C when mature
Blue leaved variety (C.cerifera) has become
available in recent years (again, visit The Palm Centre)

All of the above plants are growing in Northern Ireland ....... most of them can survive prolonged frosts down to -10 C [12 F]