Man admitting set-up is kind of cross (7)
I believe the answer is:
maltese
'kind of cross' is the definition.
'man admitting set-up' is the wordplay.
'man' becomes 'male' (**).
'admitting' means one lot of letters goes inside another.
'up' is an anagram indicator.
'set' is an anagram of 'tes'.
'male' placed around 'tes' is 'MALTESE'.
'is' is the link.
(Other definitions for maltese that I've seen before include "From Valletta, perhaps" , "Pigeon" , "European" , "Mediterranean native" , "Steal me for Mediterranean islander" .)