Extend argument for name being in record (7)
I believe the answer is:
prolong
'extend' is the definition.
('prolong' can be a synonym of 'extend')
'argument for name being in record' is the wordplay.
'argument' becomes 'pro' (pro is a kind of argument**).
'for' means one lot of letters go next to another.
'name' becomes 'n' (common abbreviation e.g. on forms).
'being in' means one lot of letters goes inside another.
'record' becomes 'log' (logging is a kind of recording).
'n' put within 'log' is 'long'.
'pro'+'long'='PROLONG'
(Other definitions for prolong that I've seen before include "Draw out" , "Extend, protract" , "Spin out" , "Extend in length" , "Lengthen in duration" .)