Initially, detectives expect wait on warrant (7)
I believe the answer is:
deserve
'warrant' is the definition.
(I've seen this before)
'initially detectives expect wait' is the wordplay.
'initially' suggests taking the first letters.
'wait' becomes 'serve' (to wait on someone is to serve them).
The initial letters of 'detectives expect' is 'de'.
'de'+'serve'='DESERVE'
'on' acts as a link.
(Other definitions for deserve that I've seen before include "Severed (anag)" , "Be worth" , "rate" , "Merit, earn" , "Show one is worthy" .)