Popular hospital dept's broken toy with no zip? (10)

I believe the answer is:

indolently

'with no zip?' is the definition.
(zip can mean energy)

'popular hospital dept's broken toy' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'hospital dept' becomes 'ENT' (Ear, Nose and Throat department).
'broken' means one lot of letters goes inside another.
'toy' becomes 'dolly' (dolly is a kind of toy).
'ent' placed inside 'dolly' is 'dolently'.
'in'+'dolently'='INDOLENTLY'

I've seen this clue in The Telegraph.

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