A customer "give-up" is a trade executed by one broker for the client of another broker and then "given-up" to the regular broker; e.g., a floor broker with discretion must have another broker execute the trade.
GIVE-UP
Meaning of GIVE-UP in English
A guide to futures and options market technology English dictionary. Английский словарь-руководство по фьючерсам и опционам рыночных технологий . 2012