Upvote:2
To be eligible for an EEA family permit you need to prove that your EEA family member is: "working, looking for work, self-employed, studying or self-sufficient".
An employment contract that has expired will not suffice for that proof. It would be a very good idea to submit proof that she is changing jobs. The new employment contract would suffice, but you could also submit the offer letter (or pay slips, but presumably she has not yet been paid by a job she has not yet started).
I would submit both the old employment contract and some proof of the new job, to show that she has been working and will continue to do so.