Assuming the work is Licensed and they have a License, their competence will have been checked by HSE - so why check it again - what happens on site is they key.

In prep' for the work they will have had to prepare detailed and site specific method statement for HSE - get that from them and make sure they stick to it - job done!

One assumes the work will require a 4-stage clearance so a independent analytical organisation will need to be involved. You can task them with managing the competency issue especially if they hold a supervisory licence. They will know what to look for and how to address any gaps that may arise. Get them in as early as possible. Do not rely on the contactor just being 'licensed'. Licence periods vary but three years is the norm, so they may be able to demonstrate their competency during the licence application but three years is a long time and competencies can easily be compromised if they go unchecked. Similarly, do not rely on the enforcing agencies to check competencies through any visits they may pay to the contractor as visit frequency can be patchy at best. That said if the contractor has experienced frequent visits/ communication from the enforcing agencies they may be a Priority Visit Contractor (PVC). Alarm bells should ring now. Behind this might lurk enforcements/ letters/ etc. The contractor should be able to furnish you with this information on request. Be aware though that all licence holders are deemed PVC when they enter the last year of their licence period.

Sorry Stephens25059, but things are a bit different in the real world. As Chris confirms, there are some shocking licensed contractors out there. When things go wrong, you should have no expectation that the HSE to be siding with you.
Sound advice from Gerry D.

The HSE Asbestos Licence Unit will appoint regional inspectors to visit new applications or renewals, the Inspectors carry out an appraisal of that organisation on the day of the assessment visit. That is fed back to the Licensing Unit, they can only make a judgement based on that. The HSE's role is not to endorse every job that has an ASB5 (notification of licensed asbestos removal) against it. In house and external auditing is an integral part of the comapny's health and safety management system. You don't just get a licence then forget about health and safety until the inspectors visit you in say three years time.
The thread poster has asked a simple question. In response to that I will forward an audit specification.

I held a supervisors license for a while and can confirm that licensed contractors vary in the quality of their risk controls, not only between contractors but also between sites.

They do dangerous work on our sites. It is perfectly reasonable to want to make sure that they aren't exposing our people to harm.