Those honourably discharged, one after army corps backed appeal (7)
I believe the answer is:
emeriti
'those honourably discharged' is the definition.
(holders of emeritus positions)
'one after army corps backed appeal' is the wordplay.
'one' becomes 'i' (Roman numeral).
'after' means one lot of letters go next to another.
'army corps' becomes 'reme' (Royal Electrical and Mechanical Engineers).
'backed' says the letters should be written in reverse.
'appeal' becomes 'it'.
'reme' written backwards gives 'emer'.
'emer'+'it'='emerit'
'i' after 'emerit' is 'EMERITI'.
(Other definitions for emeriti that I've seen before include "Persons who have been honourably discharged from public duties; time ire (anag.)" , "Honorary retired academics" , "old lecturers" , "Former professors" , "Retired title-holders" .)