Old German wants no second extension to cell (4)
I believe the answer is:
axon
'extension to cell' is the definition.
(part of a nerve cell)
'old german wants no second' is the wordplay.
'old german' becomes 'saxon' (I've seen this before).
'wants no' is a deletion indicator.
'second' becomes 's' (common abbreviation).
'saxon' with 's' taken out is 'AXON'.
(Other definitions for axon that I've seen before include "extension in cell" , "Part of cell transmitting" , "Disabling headache" , "impulsive conductor" , "Bit of a nerve!" .)