Congratulations. All the best on your new endeavour.
Background checks are different depending on the security level clearance required. The highest are the MHA, MFA, and
CPIB; they will check your references, educational background, family background, criminal records (if any), political agenda (if possible), etc.
Most will simply call your reference and maybe conduct a rudimentary background check.
There are some HR officers like that, not going to lie. In such a case, do not list them as the reference and have an answer ready for "Why did you quit your previous line of work?"
In the Public Service? Zero. We always recruit new staff every quarter to offset the potential retirees of that specific period of time, and possibly grow the company if that is what is mandated. Only when companies are closing down or being downsized is a hiring freeze a possibility.