He hopes to cultivate a relationship with IMG.
This sentence -- with a
relationship -- can't mean 'to improve the relationship' because there isn't
any relationship yet, as Richard points out. It means to start a beneficial relationship.
If the determiner is different and specific -- using the
, for example -- then we know that the relationship has already begun and that the speaker wants to improve this relationship.
So, the original sentence can't be changed to mean 'to improve the relationship,' but if the sentence is changed to include 'cultivate his
relationship -- as Jerry writes -- then there is different meaning: that the speaker wants to improve the existing relationship.
This is an important difference.