Ancient Greek bridge crossing a rivulet’s banks (7)
I believe the answer is:
spartan
'ancient greek' is the definition.
(I've seen this before)
'bridge crossing a rivulet's banks' is the wordplay.
'bridge' becomes 'span' (synonyms).
'crossing' is an insertion indicator (to cross can mean to go over or around).
'banks' means to remove the middle letters (the sides or banks of the word).
'rivulet' with its centre removed is 'rt'.
'a'+'rt'='art'
'span' placed around 'art' is 'SPARTAN'.
(Other definitions for spartan that I've seen before include "Of conditions, simple and harsh as for ancient Greeks" , "Resolute in the face of pain -- austere" , "Very strict - austere" , "Of conditions, harsh and lacking comforts" , "Not comfortable" .)