Since how much she cared for him was the driving force behind what she did through the whole movie in not killing the Russian president, killing all the other spies, and then preventing the missiles from being launched.

She didn't react visibly when he was killed, but that was because she couldn't since killing him in front of her was a test of her loyalty.

I didn't see much connection between them to justify her great efforts.

They didn't spend a lot of time on it but when he rescued her from North Korea she actually fell in love with him. That love is the only reason she went home after escaping the CIA office. When she learned he'd already been taken she knew she had no choice but to appear to follow through with the plan until she could get to him and when that failed everything else was revenge.

Not a lot of time was spent on it, but it seemed much more of a clear motivation that most revenge summer action movies bother with instead just starting with the murder of the wife/girlfriend/daughter and moving on from there.

I would rather not see the relationship and so imagine it to be earth-moving than see what appears to be a tepid relationship and wonder why it was so motivating. There was no chemistry between them that I could see. If there isn't time to demonstrate a connection, then just allude to his contributions to securing her freedom and let me imagine how their romance might have played out.