I break into the Banking industry a couple of years ago. It is not easy to enter the industry if you do not have connections or relevant skill sets. This is a very closed industry and people basically musical chair from bank to bank. Only those already working in the industry will have the relevant experience to move upwards. Therefore, you need to find a foot in. Once you are inside, it is very easy to move. From Operations to Compliance, Finance to Product Control, Project Management to Front Office Support.

For someone with no experience or connection... You can either apply the grad positions of respective banks and hopefully get a foot in. If not, taking up contract role helps alot. Many people working in the industry started out as contractor. Lastly, the longer way is to obtain the relevant experience. Banks love to hire people from MAS, Big 4, Technology Firms, Consulting Firms etc depends on your interest.

Hope this helps.