... starting with a rational methodology that's agreeable (4)
I believe the answer is:
warm
'agreeable' is the definition.
Both the answer and definition are adjectives. Maybe they are linked in a way I don't understand?
'starting with a rational methodology' is the wordplay.
'starting' suggests taking the first letters.
'rational methodology' becomes 'rm' (this might be a standard abbreviation which I don't know about).
The initial letter of 'with' is 'w'.
'w'+'a'+'rm'='WARM'
'that's' is the link.
Can you help me to learn more?
(Other definitions for warm that I've seen before include "Slightly hot" , "Friendly" , "Affectionate - balmy" , "Approaching target" , "Tepid" .)