Deprived of hat to cover Frenchman's head (6)
I believe the answer is:
bereft
'deprived' is the definition.
(I've seen this before)
'hat to cover frenchman's head' is the wordplay.
'hat' becomes 'beret' (I've seen this before).
'to cover' means one lot of letters goes inside another.
'head' indicates taking the first letters.
The first letter of 'frenchmans' is 'f'.
'beret' enclosing 'f' is 'BEREFT'.
'of' is the link.
(Other definitions for bereft that I've seen before include "Having a deep sense of loss" , "Sorrowful through loss" , "Deprived of something precious" , "Pained by the loss of someone" , "Grieving from deprivation" .)