Jacket, not a twinset (7)

I believe the answer is:

doublet

I'm a little stuck... Click here to teach me more about this clue!

'jacket' is the definition.
(doublet is a kind of jacket)

I don't understand the rest of the clue.

(Other definitions for doublet that I've seen before include "Formerly, a man's close-fitting jacket" , "Close-fitting jacket (14th to 17th century)" , "Old garment worn with hose" , "Historical jacket" , "Close-fitting padded jacket of Tudor and Stuart England" .)

I've seen this clue in the Evening Standard.

Want a hint initially instead of a full solution? Install my app