Own a part of a golf course with no name (5)
I believe the answer is:
agree
'own' is the definition.
(thesaurus)
'a part of a golf course with no name' is the wordplay.
'part of a golf course' becomes 'green' ('green' is part of 'golf course').
'with no' suggests deleting specific letters.
'name' becomes 'n' (common abbreviation e.g. on forms).
'green' with 'n' taken out is 'gree'.
'a'+'gree'='AGREE'
(Other definitions for agree that I've seen before include "Eager (anag)" , "Concur - correspond" , "'Birds in their little nest . . . . .'" , "Hold the same view" , "'Assent, concur (5)'" .)