Brought home after lake picked up (7)
I believe the answer is:
learned
'picked up' is the definition.
('learn' can be a synonym of 'pick up')
'brought home after lake' is the wordplay.
'brought home' becomes 'earned'.
'after' means one lot of letters go next to another.
'lake' becomes 'l'.
'earned' put after 'l' is 'LEARNED'.
(Other definitions for learned that I've seen before include "Highbrow" , "Full of knowledge" , "a word defining friend from Chambers?" , "Educated, scholarly" , "Gained knowledge" .)