Old dons deserve being in media, periodically (7)
I believe the answer is:
emeriti
'old dons' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.
'deserve being in media periodically' is the wordplay.
'deserve' becomes 'merit' (synonyms).
'being in' indicates putting letters inside.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
The alternating letters of 'media' are 'ei'.
'merit' placed into 'ei' is 'EMERITI'.
Can you help me to learn more?
(Other definitions for emeriti that I've seen before include "Retired title-holders" , "Esteemed quondam staff" , "honoured predecessors?" , "Former academics" , "More than one retired don" .)