Put up with short barrel round island and lake (5)
I believe the answer is:
built
'put up' is the definition.
(put up can mean to build or erect)
'short barrel round island and lake' is the wordplay.
'short barrel' becomes 'but' (I can't explain this - if you can you should believe this answer much more).
'round' indicates putting letters inside.
'island' becomes 'i'.
'and' says to put letters next to each other.
'lake' becomes 'l' (geographical abbreviation).
'i'+'l'='il'
'but' enclosing 'il' is 'BUILT'.
'with' is the link.
(Other definitions for built that I've seen before include "Constructed" , "assembled" , "Made by combining materials and parts" , "Raised" , "Erected" .)