A trio bent on making a relationship (5)
I believe the answer is:
ratio
'a relationship' is the definition.
(relationship between two numbers)
'a trio bent on' is the wordplay.
'bent' indicates anagramming the letters.
'on' is an insertion indicator (as in clothing 'on' a person).
'trio' anagrammed gives 'rtio'.
'a' going inside 'rtio' is 'RATIO'.
'making' is the link.
(Other definitions for ratio that I've seen before include "Relative proportion" , "3 relation" , "Relative magnitudes of two quantities" , "Quotient of two numbers" , "Correlation" .)