The info you've given is too incomplete for anyone to give good advice yet. So much depends on the particular circumstances, on the exact wording of the union contract, even on the applicable state & federal laws.
First and foremost: document absolutely everything possible, beginning with the situation BEFORE the new head came in, and then all incidents AFTER, including as close as possible dates, and witnesses, and gist of all conversations as accurately as possible. No one will look closely at a case without such documentation.
Next: There are higher levels of union officials. Go thru the union's "chain of command." Go quickly. And never believe their "I'll get back to you." You must bug them. Give each chain level ONE chance, and then immediately go to the next level.
Next (actually, simultaneously): Talk to every single fellow teacher about the situation and assess what, if any, collective action might be taken on your husband's behalf. Group pressure can be highly effective (the real meaning of a union). Perhaps signatures on statements, perhaps petitions to a dean, perhaps informational picket lines in strategic places – be inventive, if there's support. A day's strike in sympathy -- who knows? This stuff is a long shot but also your very best hope if it can be put into gear.
Next (actually, simultaneously): Find out if any other teachers can recommend a labor lawyer that has experience in these type of academic cases. Run don't walk, WITH your documentation, to see him/her. If nothing else call your local AFL-CIO (are you in the States?) council and ask for a recommendation.
Finally, you may have an option to sue the union for nonrepresentation if they have made no effort on a member's behalf (this is different from making a losing effort). Ask the lawyer.
Welcome to email me if you wish, firstname.lastname@example.org.
Best of luck. Above all remember, you will get nothing unless you pursue relentlessly.
--8 years, UAW chief steward, Chrysler Corp.