A fairly unimportant river runs through it (6)
I believe the answer is:
pretty
'a fairly' is the definition.
(I know that fairly can be written as pretty)
'unimportant river runs through it' is the wordplay.
I cannot quite understand how this works, but
'river' could be 'r' (abbreviation for river) and 'r' is found in the answer.
'unimportant' could be 'petty' (similar in meaning) and 'petty' is found within the leftover letters.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for pretty that I've seen before include "Daintily good-looking, maybe as a picture" , "Lovely" , "Facially attractive" , "Pleasing on the eye" , "charming to look at" .)