Bit of a lift (6)
I believe the answer is:
snatch
I believe this clue is a double definition.
'bit' is the first definition.
(I have seen 'bit of air' mean 'snatch' so perhaps 'bit' could also mean 'snatch')
'a lift' is the second definition.
(thesaurus)
'of' acts as a link.
(Other definitions for snatch that I've seen before include "Grab rudely, hastily" , "Grab, seize eagerly" , "fragment of tune" , "Seize - fragment of verse" , "Grab - wrench" .)