Get rid of small uncertainty without Britain (4,3)
I believe the answer is:
weed out
'get rid of' is the definition.
(weeding out is a kind of getting rid of)
'small uncertainty without britain' is the wordplay.
'small' becomes 'wee' ('wee' can be similar in meaning to 'small'**).
'uncertainty' becomes 'doubt' (doubt is a kind of uncertainty).
'without' suggests deleting specific letters.
'britain' becomes 'b' (common abbreviation as in GB).
'doubt' with 'b' taken out is 'dout'.
'wee'+'dout'='WEED OUT'
(Other definitions for weed out that I've seen before include "Remove unwanted elements" , "Eliminate" , "Identify and get rid of" .)