Brittle BBC boss welcomed by the old in retirement (4)
I believe the answer is:
edgy
'brittle' is the definition.
(both can mean nervous)
'bbc boss welcomed by the old in retirement' is the wordplay.
'bbc boss' becomes 'DG' (short for director-general of the BBC).
'welcomed by' is an insertion indicator (letters welcomed inside).
'the old' becomes 'ye' (resembles a historical spelling of 'the').
'in retirement' says the letters should be written in reverse (retire can mean to go back or backwards).
'ye' reversed gives 'ey'.
'dg' put into 'ey' is 'EDGY'.
(Other definitions for edgy that I've seen before include "Sharp in outline" , "Overstrung" , "ready to flap?" , "Anxious" , "Extremely" .)