Going straight home to wear wig, a bald drunk (3-7)

I believe the answer is:

law-abiding

'going straight' is the definition.
(going straight can mean following the law)

'home to wear wig a bald drunk' is the wordplay.
I cannot quite understand how this works, but
'home' could be 'in' (to be in is to be (at) home) and 'in' is found within the answer.
'a' is present in the answer.
This may be the basis of the clue (or it may be nonsense).

I've seen this clue in The Times.

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