The entrepreneur will never be able to recreate himself.
Often they look to their family to take up the mantle. However professional training and the spirit of their leader will not be repeated. Rarely perhaps, but not as a general rule.
Many will hire the next chief executive from outside, with industry experience, but often again that person will lack the thought process which allowed the entrepreneur to get where they are today.
A few entrepreneurs cover the role with promotion from inside the current organisation. This is a soft way of kicking the can down the road. That person will rarely have fresh idea, command respect nor develop the next product. It could be seen as a caretaker role.
Succession is a problem and leads oftentimes to a sale of the business to a larger trade buyer.
Any of the routes sought above have negatives and it will be down to the existing entrepreneur to choose the best worst option.
The caretake role whether by family, from outside or within allows the business to mature and perhaps be ready for sale in a few years after the entrepreneur stops driving the business further forward