DIAF
I don't work for NATS and therefore have no idea what clearance you are having to go through but, if it is a case of just giving references and showing a passport (i.e. CTC) then it can be done very quickly. If you have had to fill out a form that needs to go back to the DVA (i.e. SC or DV) then it can take between 10 weeks and 6 months.
More information is given here:
Ministry of Defence | About Defence | What we do | Security and Intelligence | Defence Vetting Agency | What we do - National Security checks
and here:
Ministry of Defence | About Defence | What we do | Security and Intelligence | Defence Vetting Agency
Cheers
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