There is no law which prevents you from joining or getting into a fresh employment while any litigation is pending regarding a previous employment in a court of competent jurisdiction. However, while submitted the form/ applying for the job, when the reason for leaving the previous job is asked specifically, then it is mandatory to disclose any information to the possible future employer regarding any litigation or issue which is pending regarding the past employment. This is so because non-disclosure of any relevant information may deem you unfit for future employment on the ground of intentionally trying to hide/conceal the said information. This rule is strictly followed in case of any criminal litigation which may be pending against you, however, in case of a service dispute, it is enough to merely mention the pendency of the case. But in your case, it seems you have disclosed the said information to the new university, so prima facie, there should be any ground for non-consideration of your candidature.
However, in order to be able to tell you the exact position, I need to review the following documents:
1. The writ petition pending before the high court regarding previous employment;
2. terms and conditions of the future employment; and
3. any correspondence between you and the future employer.
So, in your case, prima facie, there is no legal bar for you to get an employment. I suggest that you give a lawyer's drafting representation to the new university clarifying your candidature.