Barnet style in Rio had to change (6)

I believe the answer is:

hairdo

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'barnet' is the definition.
(I've seen this before)

'rio had to change' is the wordplay.
'to change' indicates an anagram.
'rio'+'had'='riohad'
'riohad' anagrammed gives 'HAIRDO'.

'style in' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for hairdo that I've seen before include "that may go with a bang?" , "Bob, perm or bouffant" , "Possibly cut" , "Style of coiffure" , "Coiffure (colloq.)" .)

I've seen this clue in The Sun.

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