It means himself/herself/itself. Word by word, this sentence reads ’the lawyer has on himself a black suit’ and the verb ha på sig means ’to wear’.
In English 'advocate' means 'to support someone publicly.' The lawyers speak on behalf of the defendant. "advokat" = "lawyer"
That's not always the case. I like Wikipedia's short definition:
An advocate is a professional in the field of law. Different countries' legal systems use the term with somewhat differing meanings. The broad equivalent in many English law-based jurisdictions could be a barrister or a solicitor.
But a dark suit and a black suit aren't necessarily the same thing.