A girl will be round the job-centre shortly (4)
I believe the answer is:
anon
'shortly' is the definition.
(synonyms)
'a girl will be round the job-centre' is the wordplay.
'a girl will' becomes 'ann' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'be round' means one lot of letters goes inside another.
'centre' means to look at the middle letters.
The central letter of 'job' is 'o'.
'ann' going around 'o' is 'ANON'.
Can you help me to learn more?
(Other definitions for anon that I've seen before include "At another time, of old" , "Shortly; unknown" , "Writer unknown" , "soon to be written" , "Incognito (abbrev)" .)