Can you describe the growing conditions it's in? Things like watering, fertilising, indoor/outdoor, type of soil, etc.

I live in Cape Town, South africa and its winter here at the moment so I'm not watering regularly because of the rain( use to water every 2nd day) . I fertilize the tree with epsom salt water and Bone Meal- Tree is outside . I actually thought the over watering was causing the discolour and only watered when soil was dry - Soil type is normal potting soil -

(I live an ocean away from you - the Indian Ocean.) Date Palms (Phoenix dactyliphera) are generally thought of as desert plants but I've seen plantations of them growing around springs and even in water. The climate has been dry though, as in hot dry desert air. But provided drainage is good and the bottom of the pot isn't sitting in water I wouldn't think over watering would be the issue. If the problem was there before you reduced the watering then not likely the soil's too dry. You can check by pushing a wooden skewer, or something similar, deep into the soil and it will show if moisture is present (or not) when you pull it out.

Is the browning on all the leaflet tips or only on some? Have you checked for insects/pests? Some you'd need a magnifying glass to get a good look at.

These look like the leaves of a Phoenix roebellenii, which is not a desert palm (actually more like a jungle palm)... still, it is a remarkably adaptable species considering its tropical origins. Unless your soil is not draining well, I doubt all the rain water your climate could muster would be too much for this species... leaf a lower one? May be normal senescence. But does look a bit like dehydration or poor water quality we get here in California during late, hot summers. Is it in a pot? might be best NOT to fertilize it too often in that condition... these generally need very little fertilization when planted in good potting soil. In deficient ground soils is a different situation, though. Recommend a dilute, general liquid fertilizer for potted palms.