Detective Sergeant, drinking more rum, walks unsteadily (7)

I believe the answer is:

dodders

'walks unsteadily' is the definition.
(I've seen this in another clue)

'detective sergeant drinking more rum' is the wordplay.
'detective sergeant' becomes 'DS' (abbreviation for detective sergeant).
'drinking' indicates putting letters inside (inserted letters are consumed or drunk).
'more rum' becomes 'odder' (rum can mean odd).
'ds' placed around 'odder' is 'DODDERS'.

I've seen this clue in The Guardian.

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