Detectives walk taking lieutenant's first shift (8)
I believe the answer is:
displace
'shift' is the definition.
(I know that shift is a kind of displace)
'detectives walk taking lieutenant's first' is the wordplay.
'detectives' becomes 'dis' (Detective Inspectors, DIs).
'walk' becomes 'pace' (pacing is a kind of walking).
'taking' means one lot of letters goes inside another.
'lieutenant's first' becomes 'l' (pst letter of 'lieutenant').
'pace' enclosing 'l' is 'place'.
'dis'+'place'='DISPLACE'
(Other definitions for displace that I've seen before include "Oust" , "Remove from usual habitat" , "Move out of position" , "Supplant" , "Succeed" .)