Mix with tramps: not very big important person (6)
I believe the answer is:
hobnob
'mix' is the definition.
(I've seen this before)
'tramps not very big important person' is the wordplay.
'tramps' becomes 'hobos' (both can mean homeless people).
'not' suggests deleting specific letters.
'very big' becomes 'os' (abbreviation for outsize).
'important person' becomes 'nob' (nob can mean an important or wealthy person).
'hobos' with 'os' taken away is 'hob'.
'hob'+'nob'='HOBNOB'
'with' is the link.
(Other definitions for hobnob that I've seen before include "Spend friendly time together" , "Mix socially with the biscuit" , "Chat with" , "mix informally" , "Socialise (especially with posher people)" .)