Vacuous babysitter Hoskins is giving lip (4)
I believe the answer is:
brim
'lip' is the definition.
(I know that lip can be written as brim)
'vacuous babysitter hoskins is' is the wordplay.
'vacuous' says to hollow out the word (remove centre letters).
'hoskins is' becomes 'I'm' (where the crossword setter is 'Hoskins').
'babysitter' with its middle taken out is 'br'.
'br'+'im'='BRIM'
'giving' is the link.
(Other definitions for brim that I've seen before include "The edge of a cup or glass" , "Top edge of a container" , "Edge or rim" , "Lip; part of a hat" , "Edge around a hat" .)