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What type of Laurel shrub do you have?

Yes, you can take cuttings from a laurel and the following article explains the process of taking cuttings from shrubs very nicely:
https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm

I would start with a soil test. This is the only way to determine what the soil may need or what to amend the soil with for plant success.

Here are some links for you.
https://www.gardeningknowhow.com/ornamental/shrubs/cherry-laurel/growing-cherry-laurels.htm
https://www.gardeningknowhow.com/extension-search/
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm

Search for more clues on the leaves of your hedge.
Are there chewing or holes in the leaves?
Yellowing or color changes?

Here are some articles that will help you pinpoint the pest or disease.

http://www.laurelhedging.com/care/pests-of-laurel.html
http://www.ipm.ucdavis.edu/PMG/GARDEN/PLANTS/englishlaurel.html

Check the watering and care with the links below.

https://www.gardeningknowhow.com/edible/herbs/bay/bay-laurel-turning-yellow.htm
https://www.gardeningknowhow.com/edible/herbs/bay/sweet-bay-leaf-tree.htm

Shothole borers can infest these plants. Look for small holes in the bark that may be oozing. You may also see signs of sawdust.
Boring damage can cause twig die back.
Chemical control does not work since the borers are under the bark.
Most recommendations are to prune out infected plant material.
If the trunk is infested, you will want to remove the shrub.
The yellowing leaves could also be watering issues.

Make sure that the soil is moist but well draining. I would check the soil instead of watering on a schedule.
I would also recommend you pull the mulch back from the trunk of the plant, at least 6 inches.
Fertilizer can be applied in spring.
Here is a link to refresh you on the care requirements.

https://www.gardeningknowhow.com/ornamental/shrubs/cherry-laurel/growing-cherry-laurels.htm

The yellowing of the leaves is generally a sign of watering issues; either too much or too little.
Even a few days of drought can cause yellowing leaves.
Active growing takes place March through October, so watering should continue through this period.
Dig down into the soil or push your hand down into the soil. The soil should be moist but not soggy. Is the ground compacted? This can hamper the water from draining away from the roots. If the roots sit in soggy soil, they will die from root rot.
If the soil is compacted you may need to dig the plant up and break up the soil. Amending the soil at that time can help future watering issues.