Baby close to tears in Tesco tickled (6)
I believe the answer is:
cosset
'baby' is the definition.
(I know that baby can be written as cosset)
'close to tears in tesco tickled' is the wordplay.
'close to' indicates one should take the final letters (the close of something is the end).
'in' indicates putting letters inside.
'tickled' is an anagram indicator (letters tickled out of place).
The last letter of 'tears' is 's'.
'tesco' with letters rearranged gives 'coset'.
's' going within 'coset' is 'COSSET'.
(Other definitions for cosset that I've seen before include "Protect overindulgently" , "Fondle" , "pet" , "Overindulge" , "Nanny" .)