Become engaged with some time-sharing (4)
I believe the answer is:
mesh
'become engaged' is the definition.
(I've seen this before)
'with some time-sharing' is the wordplay.
'with' indicates a hidden word.
'MESH' is hidden within 'some time sharing'.
(Other definitions for mesh that I've seen before include "Netting made of wire or thread" , "Net, snare" , "Engagement" , "Grid, netting" , "Become entangled - become engaged" .)