Drink that's carroty regularly getting into wee (7)
I believe the answer is:
martini
'drink' is the definition.
(martini is a kind of drink)
'carroty regularly getting into wee' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'getting into' indicates putting letters inside.
'wee' becomes 'mini' (I've seen this in another clue).
The alternate letters of 'carroty' are 'art'.
'art' inserted within 'mini' is 'MARTINI'.
'that's' is the link.
(Other definitions for martini that I've seen before include "Gin or vodka with dry vermouth" , "In glass, one's dry" , "Cocktail made with gin or vodka and vermouth" , "Alternative name for Simone Memmi, pre-Renaissance Italian painter" , "Cocktail of gin and dry vermouth" .)