Great question!
Depending on what job you apply for you may get driving qualifications during training. There's also the opportunity to gain further driving qualifications after training.
Have a look at the link below to find information tailored to your aspirations (details on driving qualifications can be found on the individual job pages under "Training for the role" and "Qualifications you could get after training").
I'm a Regular soldier, so unfortunately I can't provide any first hand experience on the Reserve application process, but I hope that's helped to answer your question until a Reserve can provide more insight.
Good luck on your journey.
https://jobs.army.mod.uk/army-reserve/available-roles/
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