French chemist providing adhesive — extremely unpopular (7)
I believe the answer is:
pasteur
'french chemist' is the definition.
(I've seen this before)
'adhesive extremely unpopular' is the wordplay.
'adhesive' becomes 'paste' (paste is a kind of adhesive).
'extremely' means to remove the middle letters (only the extremes of the word are used).
'unpopular' with its centre taken out is 'ur'.
'paste'+'ur'='PASTEUR'
'providing' acts as a link.
(Other definitions for pasteur that I've seen before include "He invented a method to stop milk causing disease" , "Louis -, nineteenth century French chemist" , "He developed the partial sterilization of milk" , "Louis --, French chemist/bacteriologist" , "French chemist and biologist (1822-1895)" .)