Retired professors showing worth in European institute (7)
I believe the answer is:
emeriti
'retired professors' is the definition.
(I've seen this before)
'worth in european institute' is the wordplay.
'worth' becomes 'merit' (merit is a kind of worth**).
'in' means one lot of letters goes inside another.
'european' becomes 'e' (abbreviation e.g. EU).
'institute' becomes 'i' (common abbreviation as in MIT).
'e'+'i'='ei'
'merit' inserted into 'ei' is 'EMERITI'.
'showing' is the link.
(Other definitions for emeriti that I've seen before include "Retired title-holders" , "Former academics" , "old lecturers" , "honoured predecessors?" , "(Of, say, professors) retired, but retaining title" .)