Agencies along The States' borders for quite a while (4)
I believe the answer is:
ages
'quite a while' is the definition.
I can't judge whether this defines the answer.
'agencies along the states' borders' is the wordplay.
'agencies along' becomes 'age' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'borders' suggests taking the first letters (I've seen 'border' mean this).
The initial letter of 'states' is 's'.
'age'+'s'='AGES'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for ages that I've seen before include "Indefinitely long time" , "Matures" , "Donkey's years" , "Rock of - - (hymn)" , "Gets older" .)