1. If the person is going to manage a pub owned by a company then it is up to the company to make whatever credit checks they think necessary. I would expect them to do a full one & refuse someone who has just been discharged unless there are good reasons for accepting them.
2. If the person is going to run a pub they own, the question that arises is where did the money come from to buy it - their assets should all have gone into the bankruptcy.
3. Neither of the above points answer your query about getting a license. I'm not sure, but think this is a matter for the local authority issuing the license & they may have different criteria in different areas.
4. The Trustee's statement is a record of the Insolvency Service's assessment of the amount of the bankrupt's debts and assets. It will be based on information provided by the bankrupt plus the result of any investigation done by the Trustee. If it shows nil under assets & the bankrupt ends up having sufficient money to buy a pub a year after discharge, there could be a cause to ask questions. However, it could be that the money has been provided by someone else.