We had that happen at one of our rentals, Was told this can happen sometimes as they don't last forever..
We also had this happen at our own house when we installed a gate, it disturbed the roots i think. Anyway, the whole hedge lost all it's leaves and looked dead. After 6 months, i was going to pull it out, but as i checked some of the branches by scrapping the bark off, some were still green but most were dead.
I applied chicken manure pellets, blood and bone and seaweed solution every 3 weeks.
Well now it's fully green and even flowered.

So i suggest scrapping a little of those dead looking branches and checking if they are alive, if they are, give it some fertilizer and cross your fingers.

Not sure what type of hedge it is, but ours is a Conifer.

That looks like the dwarf Murraya, Murraya paniculata 'min-min' I think it's called. I have 2 hedges of that and periodically sections die off, which I simply cut out. It seems to occur mainly during long dry spells. Watering helps but I also think they have a limited life span. If you can id. the hedge we could be more accurate.
B.

This looks like a Murraya paniculata they grow to 1.5 meters tall they will dye back in sections by going yellow but will bounce back.