Divorce was allowed by Moses.
Not by Jesus - Mark 10
But does the cause of divorce automatically assume remarriage? It is one thing to nullify the contract, it is quite another to infer eligibility to engage in another contract. Rom 7 interprets divorce according to Torah quite harshly: The woman is bound to the man until death - divorce or no. Upon the man's death, she is free to marry and free from committing adultery...
One can infer the same for the man, though it is made murky in that a man can, in many Biblical instances, have more than one wife - But if the woman he might intend to marry is a divorcee, and not yet widowed, he is certainly committing adultery, just the same as she.