Matthew McNamara, 42, was jailed for 24 weeks for numerous breaches of a Criminal Behaviour Order, barring him from certain anti-social acts in the area.
Now, ahead of his release next month, police have applied tot he courts to place further restrictions on him until May 2020.
The order now bars McNamara from begging anywhere in the Humberside force area and from entering Princes Avenue, where he is accused of causing problems to residents and businesses.
He is also barred from behaving anti-socially or drinking on the street anywhere in the Humberside force area.
PC Scott Greenwood said: "Matthew McNamara is a persistent and aggressive beggar who has caused a lot of problems for residents and businesses in Princes Avenue.
“We know the impact that his behaviour has had and that’s why we have acted quickly to ask the courts to change his order, as removing him from the area will have a hugely positive impact.
“We’re also helping him to understand that he we will not tolerate him making others feel uncomfortable or uneasy and that he has to change his ways.”
PC Scott said the force worked with local authorities, health services and charities to offer support to "people who find themselves on the streets".
He said: "However, when people are persistently begging or behaving in a way that’s causes distress to others who are trying to go about their business, then we will take action.
“Since Mr McNamara has been in prison, the area has looked and felt a much better place to be and we will continue to act swiftly to deal with anyone whose behaviour impacts on this."