Asleep, chap in Dortmund half gone (7)
I believe the answer is:
dormant
'asleep' is the definition.
(similar in meaning)
'chap in dortmund half gone' is the wordplay.
'chap' becomes 'Man' (chap can mean a man).
'in' indicates putting letters inside.
'half gone' means to take half the letters.
'dortmund' halved is 'dort'.
'man' going inside 'dort' is 'DORMANT'.
(Other definitions for dormant that I've seen before include "Lying inactive as if in sleep" , "Lethargic" , "Temporarily quiet" , "Comatose" , "Mordant about lying inactive" .)