Trendy university in London area (7)
I believe the answer is:
popular
'trendy' is the definition.
(I've seen this before)
'university in london area' is the wordplay.
'university' becomes 'u' (abbreviation for university).
'in' is an insertion indicator.
'london area' becomes 'poplar' (I've seen this before).
'u' placed inside 'poplar' is 'POPULAR'.
(Other definitions for popular that I've seen before include "Demotic" , "Widely admired" , "Hot" , "Trendy" , "Democratic - of general appeal" .)