Hebe pruned recentlyThis is Hebe (buxifolia)? This is one of my all time favorite shrubs. What zone are you in? These do well only as low as 5. They are evergreen thus those leaves are subjected to too cold temperatures below 5. They need excellent drainage meaning raised beds, not raised beds with lumber or brick, just fluffed up soil that is a good foot higher than the original surface. It will reduce to about 6 inches. A shallow trench around the base of the bed which doubles as a crisp clean edge defining the lawn...if that is nearby. Hebe loves an acid soil. Like hydrangeas. Lawn loves a bit more alkaline of a soil.
I wouldn't bother taking cuttings and vegetatively reproducing. I'd make plant beds, test the pH of the soil, purchase at least 4 or 5 plants. Make a grouping on one side of the landscape with one or two or more balancing that first grouping on the other side or nearby. This shrub is excellent for a soft hedge. No pruning except the wayward branch. Plant in a staggered line no closer than 3 feet apart...forming equilateral triangles between shrubs. Don't do straight lines of anything. Breathtaking super duper 'skeleton' plant for the landscape. This shrub will pull together any motley landscape perfectly, low maintainance if given the proper pH, proper fertilizer in the proper zone. Needs water at the beginning until established!
Quick point to make. The picture of your old mature shrub shows a very healthy shrub. BUT, I would prune to allow the lower skirt of that shrub to be wider than the top. This guy would take a few delicate prunings to get him in the correct form so that those leaves on the bottom get as much light, or close to as much light as the top leaves on that shrub. Leaves that produce more food for the plant because they get more sun will be taken care of before leaves and branches not able to produce as much food. Chemicals/nutrients when low are always transported to the new growth, the top, first. If the soil is too low in the necessary chemicals (NPK and a good dozen microchemicals/nutrients from a balanced fertilizer but again a little too much is death, a little too little is a slower death) only the top growth the big producers of food for the plant get what is available. The bottom growth will be ignored. Even with plenty of correct chemistry, proper pH (wrong pH and even though the chemistry is there is will be made unavailable to the plant), the plant will always send more water, nutrients/chemicals to the producers and ignore those that don't produce much in the way of food for the plant. The trick is to always have the top of a shrub narrower than the bottom. Even for formal hedges! Natural look is like an upside down salad bowl, like half of a sphere. This is the most healthy form for shrubs. The picture I took is not bad for pruning but it would be better if there was a gentle continuous line from the very bottom to the top. See the shade beneath the curve going back into the shrub? This pruning should only be done at the most once per year. Usually that is enough unless the size needs containment or there is a wayward branch poking up. Hebe looks best not newly pruned...I use floral snips to prune after the initial shaping.