Our date palm (approx 8 years old and previously healthy) is throwing up new shootsl but they are turning brown t is i

As its eight years old, its quite possible that it needs more root room than the half barrel allows it. To my everlasting shame, I see you live in Denbighshire, but confess I have no idea where that is, my point being, here in the south, we're in drought, it's beginning to look like the sahara - a plant with roots crammed into a pot cannot retain water so well, so yours may be drying out very rapidly, and not able to grow-on the new shoots.