What to write in CV when transferring between schools?
The problem is I have not been student at New University since 2010 and I don't want to say that I'm a first year student. Also since I didn't get any degree from Old University I cannot have a separate entry for it.


Why does it matter whether you got a degree from Old University?  There's no rule that says the education section of your CV can only be organized by degree.  You just need to be clear and honest.

What you propose doesn't seem inappropriate, but I think this might be slightly clearer:

2014-2016 (expected) PhD in Computer Science from New University

2010-2014 PhD student at Old University (transferred to New University)

2007-2010 MS in Computer Engineering from Another University