A row, not the first, in public sale (7)
I believe the answer is:
auction
'public sale' is the definition.
(sale of items to the public)
'a row not the first' is the wordplay.
'row' becomes 'ruction'.
'not the first' means to remove the first letter.
'ruction' with its initial letter removed is 'uction'.
'a'+'uction'='AUCTION'
'in' is the link.
(Other definitions for auction that I've seen before include "A lot will be seen in this" , "Public sale at which bids are made" , "Public bidding sale" , "Public sale by bid" , "Use caution at public sale" .)