Party men approaching dull person easily put upon (7)
I believe the answer is:
doormat
'person easily put upon' is the definition.
(doormat can mean a subservient person)
'party men approaching dull' is the wordplay.
'party' becomes 'do' (do is a kind of party).
'men' becomes 'or' (military abbreviation for Other Ranks).
'approaching' means one lot of letters go next to another.
'dull' becomes 'mat' (mat as opposed to glossy).
'do'+'or'+'mat'='DOORMAT'
(Other definitions for doormat that I've seen before include "Submissive person (colloq.)" , "seen walking in?" , "Badly treated but uncomplaining person" , "Drudge" , "Lackey" .)