The chap dropped round at the beginning of the week (6)
I believe the answer is:
fellow
'the chap' is the definition.
('fellow' can be a synonym of 'chap')
'dropped round at the beginning of the week' is the wordplay.
'dropped' becomes 'fell' (I've seen this before).
'round' becomes 'o' (round can mean a round object**).
'at the beginning of' says to take the initial letters (I've seen 'at the beginning' mean this).
The first letter of 'week' is 'w'.
'fell'+'o'+'w'='FELLOW'
(Other definitions for fellow that I've seen before include "Senior member of a college or university" , "college type" , "Academic chap?" , "Comrade" , "Colleague" .)