Idiosyncratic of Luton, say, losing top spot (3)
I believe the answer is:
own
'idiosyncratic' is the definition.
(idiosyncratic means personal or one's own)
'luton say losing top spot' is the wordplay.
'luton say' becomes 'town' (Luton is a town).
'losing top spot' means to remove the first letter (the letter at the top is removed).
'town' with its initial letter removed is 'OWN'.
'of' is the link.
(Other definitions for own that I've seen before include "Have in one's possession" , "Keep" , "Personal; possess" , "Control" , "Posses" .)