The quick answer is - not always.
Each SIA Licence application is judged on a case-by-case basis with all information forming part of the decision. Getting an SIA Licence with a criminal record will depend on a few different factors:
Whether your offence is relevant to your application.
The sentence given to you.
Was the offence recent?
The relevance of an offence will also be taken in to account.
What does relevance of a criminal record mean when it comes to getting an SIA Licence with a criminal record? Well, this means whether your criminal record shows that you may not have the temperament to work in the security industry.
So, this means that if your criminal record is for something relatively minor it may not factor too much in the decision.
However, if your criminal record has a violent offence this may become a factor that means you will be less likely to get a license. Read more here: https://www.get-licensed.co.uk/get-daily/can-i-get-an-sia-licence-with-a-criminal-record/