Tree surgery is not a regulated industry which means you can hire anyone you see fit to carry out the work.
The downside of this is that anyone can call themselves a tree surgeon and will largely get away with poor quality or dangerous work. They likely won't have the skill, knowledge and expertise of someone who is qualified and professional. Furthermore, poor tree work will potentially cost you a lot more over the ensuing years after the work is carried out or even cause damage to property or people.
Tree work can sometimes be considered expensive but a skilled tree surgeon will always be worth the investment over an unskilled chancer, regardless of the cost difference.
Always take recommendations and if not available, check who you are hiring.

The short answer is if you employ a tree surgeon and they do not have nptc qualification in use of chainsaws in harness and Ariel rescue they are not insured. The ground worker also needs Ariel rescue incase of an accident. If the ground worker does not hold this qualification ,again the insurance is void and therefore you are employing unskilled and unqualified people.

Anybody carrying out any form of tree work should carry the correct qualifications to assure the job is done safely and to a high standard.

Monkey Tree Care LTD hit the nail on the head. Great answer

Tree Surgery can be very dangerous work.
As a qualified Tree Surgeon I would always advise that any works carried out are carries out by a qualified professional but these qualifications are not common knowledge.
So, before you have any aerial works carried out on your tree/s, check they have a the relevant NPTC qualifications in 'using a saw from a rope and harness'.
If they don't have this, I'd go elsewhere...