What barber might offer that'll save time? (5,3)
I believe the answer is:
short cut
I believe this is a double definition.
'what barber might offer' is the first definition.
(a barber might offer a short hair cut)
'that'll save time?' is the second definition.
(I've seen this before)
(Other definitions for short cut that I've seen before include "What skinhead asks for" , "crew, possibly" , "Time- or distance-saving route" , "rat run?" , "that'll save time?" .)