Lawyers representing the parties made submissions yesterday before Justice Horace Marsh.
When the hearing resumes today, the lawyers will continue their submissions.
Clarke retired from the bank on November 1 and it was agreed that the issue of his retirement package would go to arbitration.
He is contending that he received a letter from the head office in Canada that he is to leave the house and hand over the motor cars by July 31.
Clarke says in court documents that if the bank is not restrained, he fears he will be evicted from the house.
When Clarke came before the Supreme Court earlier this year, the parties arrived at a consent order which allows Clarke to remain in possession of the house and motor cars until the Supreme Court makes a ruling.