Romance is nothing connected with business (4,6)
I believe the answer is:
love affair
'romance' is the definition.
(synonyms)
'nothing connected with business' is the wordplay.
I cannot quite understand how this works, but
'nothing' could be 'love' (love means zero in tennis) and 'love' is present in the answer.
'business' could be 'affair' (I've seen this before) and 'affair' is found in the answer.
No letters remain.
This explanation may well be incorrect...
'is' is the link.
Can you help me to learn more?
(Other definitions for love affair that I've seen before include "Romance" , "A (short?) romantic relationship" .)