Relationship with fifty-one first-class offspring (7)
I believe the answer is:
liaison
'relationship' is the definition.
(I know that liaison is a type of sexual relationship)
'with fifty-one first-class offspring' is the wordplay.
'with' means one lot of letters go next to another.
'fifty one' becomes 'LI' (Roman numerals).
'first class' becomes 'ai' (A1 - top quality).
'offspring' becomes 'son' (male offspring).
'li'+'ai' is 'liai'.
'liai'+'son'='LIAISON'
(Other definitions for liaison that I've seen before include "Co-operation; love affair" , "carryon" , "Secret love-affair" , "Mutual communication and co-operation" , "Communication between people or organisations" .)