Nero's not included in proper names for baby? (6)

I believe the answer is:

pamper

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'for baby?' is the definition.
('pamper' can be a synonym of 'baby')

I can't explain the rest of the clue.

(Other definitions for pamper that I've seen before include "Treat luxuriously" , "Treat indulgently" , "Treat with over-indulgence" , "'Indulge, spoil (6)'" , "Treat with excessive indulgence" .)

I've seen this clue in The Irish Times.

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