I read "current secret clearance required" in a blog and I don't understand this expression. What does it mean?
"Secret clearance" is a type of security clearance. It's a qualification government agencies can give to you. If you have this qualification, you're allowed to see privileged information.
Security clearance levels are used as part of a method to control access to information that should not be freely available to all personnel.
This is from a page about United States security clearance, and the term is also used in some other countries, so the exact definition may depend on what country you're talking about. But this should give you the general idea, in any case.
If enough time passes, your security clearance can expire, and then you won't have the qualification anymore. If that happens, your security clearance will no longer be "current". The blog is saying that this kind of security clearance is required for something, and it cannot be expired.
Required for what? It could be for a job―but see Adam's comment below for another possibility.