Rambling thickets beginning to swamp rural areas (3,6)
I believe the answer is:
the sticks
'rural areas' is the definition.
(I've seen this before)
'rambling thickets beginning to swamp' is the wordplay.
'rambling' indicates an anagram.
'beginning to' indicates taking the first letters.
The first letter of 'swamp' is 's'.
'thickets' is an anagram of 'thestick'.
'thestick'+'s'='THE STICKS'
(Other definitions for the sticks that I've seen before include "They limit goals" , "rural area" , "rural areas" , "backward area" , "country areas" .)