Briefly worry people in the pink? (9)
I believe the answer is:
carnation
'the pink?' is the definition.
(carnation is a kind of pink)
'briefly worry people' is the wordplay.
'briefly' means to remove the last letter.
'worry' becomes 'care' (eg without a care means without a worry).
'people' becomes 'nation' ().
'care' with its final letter taken off is 'car'.
'car'+'nation'='CARNATION'
'in' is the link.
(Other definitions for carnation that I've seen before include "Flower suitable for buttonhole ..." , "Oscar Wilde wore a green one" , "Pink - garden flower" , "Feature of many a wedding" , "Not in a car (anag) - plant" .)