Having no issue with Kid Rock initially in charge (5-4)

I believe the answer is:

child-free

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'rock initially in charge' is the definition.
I don't know anything about this answer so I can't judge whether this works.

'having no issue with kid' is the wordplay.
'having no issue' becomes 'free' (I can't justify this - if you can you should believe this answer much more).
'with' means one lot of letters go next to another.
'kid' becomes 'child' (synonyms).
'free' put after 'child' is 'CHILD-FREE'.

Can you help me to learn more?

I've seen this clue in The Guardian.

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